2025/06/23 更新

写真a

オザワ　トオル
小澤　徹
所属
理工学術院 先進理工学部
職名
教授
学位
理学博士 ( 京都大学（1990年03月） )
ホームページ
http://www.ozawa.phys.waseda.ac.jp/index2.html

経歴

  • 2008年09月
    -
    継続中

    早稲田大学理工学術院先進理工学部応用物理学科 教授

  • 2025年04月
    -
    継続中

    北海道大学 名誉教授

  • 2008年
    -
    継続中

    大学院先進理工学研究科物理学及応用物理学専攻 担当

  • 2008年
    -
    継続中

    大学院基幹理工学研究科数学応用数理専攻 兼担 現在に至る

  • 1995年04月
    -
    　

    北海道大学大学院理学研究科 教授（数学専攻数理解析学講座）

  • 1993年04月
    -
    　

    北海道大学理学部 助教授（数学教室位相解析講座）

  • 1992年04月
    -
    　

    北海道大学理学部 講師（数学教室位相解析講座）

  • 1990年06月
    -
    　

    京都大学数理解析研究所 助手（応用解析第一研究部門）

  • 1988年04月
    -
    　

    名古屋大学理学部 助手（数学教室解析学第一講座）

▼全件表示

学歴

  • 1988年03月
    -
    　

    京都大学大学院理学研究科数理解析専攻博士課程 中途退学  

  • 1986年04月
    -
    　

    京都大学大学院理学研究科数理解析専攻博士課程 進学  

  • 1986年03月
    -
    　

    京都大学大学院理学研究科数理解析専攻修士課程 修了  

  • 1984年04月
    -
    　

    京都大学大学院理学研究科数理解析専攻修士課程 入学  

  • 1984年03月
    -
    　

    早稲田大学理工学部物理学科 卒業 (応用物理学科 飯野理一・堤正義研究室)  

  • 1980年04月
    -
    　

    早稲田大学理工学部物理学科 入学  

  • 1980年03月
    -
    　

    早稲田大学高等学院 卒業  

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委員歴

  • 2021年
    -
    継続中

    核融合科学研究所  運営会議 委員

  • 2021年
    -
    2023年

    日本学術会議  物理学委員会 物性物理学・一般物理学分科会 プラズマサイエンス小委員会 副委員長

  • 2021年
    -
    2023年

    日本学術会議  数理科学委員会 数学分科会 委員長

  • 2021年
    -
    2023年

    東京理科大学  総合研究機構 アドバイザリー委員会 委員

  • 2020年
    -
    2023年

    日本学術会議  数理科学委員会 委員長

  • 2019年
    -
    2023年

    京都大学  数理解析研究所 運営委員会委員

  • 2019年
    -
    2023年

    京都大学  数理解析研究所 専門委員会委員

  • 2016年
    -
    2023年

    Science Council of Japan  Council Member

  • 2016年
    -
    2023年

    日本学術会議  会員

  • 2006年
    -
    2023年

    日本学術会議  数理科学委員会 数学分科会 委員

  • 2006年
    -
    2023年

    日本学術会議  数理科学委員会 委員

  • 2006年
    -
    2023年

    Japan National Committee for IMU  Committee Member

  • 2006年
    -
    2023年

    国際数学連合(IMU) 国内委員会  委員

  • 2017年
    -
    2020年

    日本学術会議  科学者委員会 研究計画・研究資金検討分科会 委員

  • 2017年
    -
    2020年

    日本学術会議  数理科学委員会 数学分科会 副委員長

  • 2017年
    -
    2020年

    日本学術会議  数理科学委員会 副委員長

  • 2012年
    -
    2020年

    日本学術会議  数理科学委員会 IMU分科会 委員長

  • 2012年
    -
    2020年

    Japan National Committee for IMU  Chair

  • 2012年
    -
    2020年

    国際数学連合(IMU) 国内委員会  委員長

  • 2015年
    -
    2019年

    東京理科大学  総合研究機構 アドバイザリー委員会委員

  • 2013年
    -
    2017年

    京都大学  数理解析研究所 運営委員会委員

  • 2009年
    -
    2017年

    京都大学  数理解析研究所 専門委員会委員

  • 2016年
    　
    　

    日本数学会  解析学賞選考委員長代理

  • 2016年
    　
    　

    日本学術会議  学術の大型研究計画検討分科会・数理科学分野の大型研究計画評価小分科会 幹事

  • 2014年
    -
    2016年

    日本数学会  解析学賞選考委員

  • 2006年
    -
    2016年

    Science Council of Japan  Associate Member

  • 2006年
    -
    2016年

    日本学術会議  連携会員

  • 2015年
    　
    　

    日本数学会  解析学賞選考委員長

  • 2014年
    　
    　

    日本物理学会  第70回年次大会実行委員

  • 2008年
    -
    2011年

    日本数学会  教育研究資金問題検討委員会運営委員

  • 2008年
    -
    2010年

    日本数学会  福原賞選考委員会 選考委員長

  • 2006年
    -
    2009年

    Mathematical Society of Japan  Board of Trustees, Committee of International Relations

  • 2006年
    -
    2009年

    日本数学会  理事 国際交流担当, MSJ Memoirs担当

  • 2005年
    -
    2008年

    Mathematical Society of Japan  Division of Functional Equations Chair

  • 2005年
    -
    2008年

    日本数学会  函数方程式論分科会 連絡責任評議員

  • 2005年
    -
    2008年

    日本数学会  評議員

  • 2003年
    -
    2008年

    Mathematical Society of Japan  Division of Functional Equations Committee Member

  • 2003年
    -
    2008年

    日本数学会  函数方程式論分科会委員

  • 1997年
    　
    　

    日本数学会  評議員

▼全件表示

所属学協会

  • 　
    　
    　

    国際解析・応用・計算学会 (International Society for Analysis, its Applications and Computation)

  • 　
    　
    　

    米国数学会 (American Mathematical Society)

  • 　
    　
    　

    日本数学会 (Mathematical Society of Japan)

研究分野

  • 基礎解析学 / 数理解析学

研究キーワード

  • 数理物理

  • 調和解析

  • 非線型偏微分方程式

受賞

  • 日本数学会賞春季賞（日本数学会）

    1998年03月  

  • 古河三水賞（古河三水会グループ）

    1984年03月  

メディア報道

  • キタノ工務店

    テレビ・ラジオ番組

    フジテレビ  

    2014年10月

 

論文

  • Asymptotic behavior of global solutions to the complex Ginzburg–Landau type equation in the super Fujita-critical case

    Ryunosuke Kusaba, Tohru Ozawa

    Evolution Equations and Control Theory   14 ( 2 ) 210 - 245  2025年04月  [査読有り]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Global \( {H^2}\)-Solutions for the Generalized Derivative NLS on \(\mathbb T\)

    Masayuki Hayashi, Tohru Ozawa, Nicola Visciglia

    SIAM Journal on Mathematical Analysis   57 ( 2 ) 1483 - 1501  2025年03月  [査読有り]

    DOI

  • Refined Interpolation Inequality in Besov Spaces With Applications to the Gagliardo–Nirenberg Inequality

    Tohru Ozawa, Taiki Takeuchi

    Asymptotic Analysis   141 ( 2 ) 119 - 131  2025年01月  [査読有り]

    　概要を見る

    We consider the interpolation inequality with respect to the regularity index [Formula: see text] in homogeneous Besov spaces [Formula: see text]. By choosing a general summability index [Formula: see text] and estimating carefully, we reveal a precise representation of the constant appearing in the interpolation inequality. As an application of the refined interpolation inequality, we show a generalization of the Gagliardo–Nirenberg inequality in homogeneous Besov spaces given by Wadade (2009) .

    DOI

  • Global Strong Solutions of the Coupled Klein-Gordon-Schrödinger Equations

    Tohru Ozawa, Kenta Tomioka

    Funkcialaj Ekvacioj   67 ( 3 ) 229 - 265  2024年12月  [査読有り]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Low regularity solutions to the logarithmic Schrödinger equation

    Rémi Carles, Masayuki Hayashi, Tohru Ozawa

    Pure and Applied Analysis   6 ( 3 ) 859 - 871  2024年10月  [査読有り]  [国際誌]  [国際共著]

    DOI

    Scopus

    2
    被引用数
    (Scopus)

  • New instability, blow-up and break-down effects for Sobolev-type evolution PDE: asymptotic analysis for a celebrated pseudo-parabolic model on the quarter-plane

    Andreas Chatziafratis, Tohru Ozawa

    Partial Differential Equations and Applications   5 ( 5 )  2024年09月  [査読有り]  [国際誌]  [国際共著]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • A new proof of the Gagliardo–Nirenberg and Sobolev inequalities: Heat semigroup approach

    Tohru Ozawa, Taiki Takeuchi

    Proceedings of the American Mathematical Society, Series B   11 ( 33 ) 371 - 377  2024年07月  [査読有り]  [国際誌]

    　概要を見る

    <p>We give a new proof of the Gagliardo–Nirenberg and Sobolev inequalities based on the heat semigroup. Concerning the Gagliardo–Nirenberg inequality, we simplify the previous proof by relying only on the - estimate of the heat semigroup. For the Sobolev inequality, we consider another approach by using the heat semigroup and the Hardy inequality.</p>

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • The Cauchy Problem for the Logarithmic Schrödinger Equation Revisited

    Masayuki Hayashi, Tohru Ozawa

    Annales Henri Poincaré   26   1209 - 1238  2024年06月  [査読有り]  [国際誌]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Representation formulae for the higher-order Steklov and $L^{2^m}$-Friedrichs inequalities

    Tohru Ozawa, Durvudkhan Suragan

    Asian Journal of Mathematics   28 ( 1 ) 93 - 102  2024年  [査読有り]

    DOI

  • A note on 2D Navier-Stokes system in a bounded domain

    Jishan Fan, Tohru Ozawa

    AIMS Mathematics   9 ( 9 ) 24908 - 24911  2024年  [査読有り]  [国際誌]  [国際共著]

    　概要を見る

    <p lang="fr">&lt;p&gt;This paper poses a new question and proves a related result. Particularly, the nonexistence of a nontrivial time-periodic solution to the Navier–Stokes system is proved in a bounded domain in $ \mathbb{R}^2 $.&lt;/p&gt;</p>

    DOI

    Scopus

  • Inverse problems of identifying the time-dependent source coefficient for subelliptic heat equations

    Mansur I. Ismailov, Tohru Ozawa, Durvudkhan Suragan

    Inverse Problems and Imaging   18 ( 4 ) 813 - 823  2024年  [査読有り]  [国際共著]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Rigorous analysis of the unified transform method and long-range instabilities for the inhomogeneous time-dependent Schrödinger equation on the quarter-plane

    Andreas Chatziafratis, Tohru Ozawa, Shou-Fu Tian

    Mathematische Annalen   389 ( 4 ) 3535 - 3602  2023年10月  [査読有り]  [国際誌]  [国際共著]

    DOI

    Scopus

    9
    被引用数
    (Scopus)

  • Refined Decay Estimate and Analyticity of Solutions to the Linear Heat Equation in Homogeneous Besov Spaces

    Tohru Ozawa, Taiki Takeuchi

    Journal of Fourier Analysis and Applications   29 ( 5 )  2023年09月  [査読有り]

    　概要を見る

    Abstract

    The heat semigroup $$\{T(t)\}_{t \ge 0}$$ defined on homogeneous Besov spaces $$\dot{B}_{p,q}^s(\mathbb {R}^n)$$ is considered. We show the decay estimate of $$T(t)f \in \dot{B}_{p,1}^{s+\sigma }(\mathbb {R}^n)$$ for $$f \in \dot{B}_{p,\infty }^s(\mathbb {R}^n)$$ with an explicit bound depending only on the regularity index $$\sigma &gt;0$$ and space dimension n. It may be regarded as a refined result compared with that of the second author (Takeuchi in Partial Differ Equ Appl Math 4:100174, 2021). As a result of the refined decay estimate, we also improve a lower bound estimate of the radius of convergence of the Taylor expansion of $$T(\cdot )f$$ in space and time. To refine the previous results, we show explicit pointwise estimates of higher order derivatives of the power function $$|\xi |^{\sigma }$$ for $$\sigma \in \mathbb {R}$$. In addition, we also refine the $$L^1$$-estimate of the derivatives of the heat kernel.

    DOI

    Scopus

    2
    被引用数
    (Scopus)

  • Weighted estimates and large time behavior of small amplitude solutions to the semilinear heat equation

    Ryunosuke Kusaba, Tohru Ozawa

    Differential Equations & Applications   ( 3 ) 235 - 268  2023年09月  [査読有り]

    DOI

  • Long time behavior of a 2D Ginzburg-Landau model with fixed total magnetic flux

    Jishan Fan, Tohru Ozawa

    International Journal of Mathematical Analysis   17 ( 3 ) 109 - 117  2023年09月  [査読有り]

    DOI

  • Charge conjugation approach to scattering for the Hartree type Dirac equations with chirality

    Yonggeun Cho, Seokchang Hong, Tohru Ozawa

    Journal of Mathematical Physics   64 ( 2 ) 021508 - 021508  2023年02月  [査読有り]

    　概要を見る

    We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential derived from the pseudoscalar field. We establish scattering for large data but with a relatively small part of the initial data associated with charge conjugation by exploiting the null structure induced by the chiral operator.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Revisiting the Rellich inequality

    Neal Bez, Shuji Machihara, Tohru Ozawa

    Mathematische Zeitschrift   303 ( 2 )  2023年01月  [査読有り]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Blow-up solutions for a class of divergence Schrödinger equations with intercritical inhomogeneous nonlinearity

    Bowen Zheng, Tohru Ozawa, Jian Zhai

    Journal of Mathematical Physics   64 ( 1 ) 011502 - 011502  2023年01月  [査読有り]

    　概要を見る

    In this article, we study a class of divergence Schrödinger equations with intercritical inhomogeneous nonlinearity [Formula: see text] where 2 − n &lt; b &lt; 2, c ≥ b − 2, and 2(2 − b) − bp &lt; np − 2 c &lt; (2 − b)( p + 2). We prove the blow-up of radial solutions for the negative energy by using a virial-type estimate. In addition, we derive a generalized Gagliardo–Nirenberg inequality and use it to establish the general blow-up criteria for radial solutions with non-negative energy.

    DOI

    Scopus

    2
    被引用数
    (Scopus)

  • Vanishing dispersion limit for Schrödinger-improved Boussinesq system in two space dimensions

    Tohru Ozawa, Kenta Tomioka

    Asymptotic Analysis   130 ( 3-4 ) 427 - 437  2022年11月  [査読有り]

    　概要を見る

    We study the vanishing dispersion limit of strong solutions to the Cauchy problem for the Schrödinger-improved Boussinesq system in a two dimensional domain. We show an explicit representation of limiting profile in terms of the initial data. Moreover, the first approximation is also represented as a pair of solutions of a linear system with coefficients and forcing term given by the limiting profile.

    DOI

  • Inverse abstract Cauchy problems

    Tohru Ozawa, Joel E. Restrepo, Durvudkhan Suragan

    Applicable Analysis   101 ( 14 ) 4965 - 4969  2022年09月  [査読有り]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Remarks on the Navier-Stokes equations in space dimension 𝑛≥3

    Jishan Fan, Tohru Ozawa

    Proceedings of the American Mathematical Society, Series B   9 ( 30 ) 317 - 324  2022年07月  [査読有り]

    　概要を見る

    <p>In this paper, we prove some new -estimates of the velocity by the technique of -energy method.</p>

    DOI

    Scopus

  • Schrödinger-improved Boussinesq system in two space dimensions

    Tohru Ozawa, Kenta Tomioka

    Journal of Evolution Equations   22 ( 2 )  2022年06月  [査読有り]

    　概要を見る

    Abstract

    We study the Cauchy problem for the Schrödinger-improved Boussinesq system in a two-dimensional domain. Under natural assumptions on the data without smallness, we prove the existence and uniqueness of global strong solutions. Moreover, we consider the vanishing “improvement” limit of global solutions as the coefficient of the linear term of the highest order in the equation of ion sound waves tends to zero. Under the same smallness assumption on the data as in the Zakharov case, solutions in the vanishing “improvement” limit are shown to satisfy the Zakharov system.

    DOI

    Scopus

    3
    被引用数
    (Scopus)

  • Small data scattering of 2d Hartree type Dirac equations

    Yonggeun Cho, Kiyeon Lee, Tohru Ozawa

    Journal of Mathematical Analysis and Applications   506 ( 1 ) 125549 - 125549  2022年02月  [査読有り]

    DOI

    Scopus

    6
    被引用数
    (Scopus)

  • Well-posedness for the Chern-Simons-Schrödinger equations

    Jishan Fan, Tohru Ozawa

    AIMS Mathematics   7 ( 9 ) 17349 - 17356  2022年  [査読有り]

    　概要を見る

    <p lang="fr">&lt;abstract&gt;&lt;p&gt;First, we prove uniform-in-$ \epsilon $ regularity estimates of local strong solutions to the Chern-Simons-Schrödinger equations in $ \mathbb{R}^2 $. Here $ \epsilon $ is the dispersion coefficient. Then we prove the global well-posedness of strong solutions to the limit problem $ (\epsilon = 0) $.&lt;/p&gt;&lt;/abstract&gt;</p>

    DOI

  • Magnetohydrodynamics approximation of the compressible full magneto- micropolar system

    Jishan Fan, Tohru Ozawa

    AIMS Mathematics   7 ( 9 ) 16037 - 16053  2022年  [査読有り]

    　概要を見る

    <p lang="fr">&lt;abstract&gt;&lt;p&gt;In this paper, we will use the Banach fixed point theorem to prove the uniform-in-$ \epsilon $ existence of the compressible full magneto-micropolar system in a bounded smooth domain, where $ \epsilon $ is the dielectric constant. Consequently, the limit as $ \epsilon\rightarrow0 $ can be established. This approximation is usually referred to as the magnetohydrodynamics approximation and is equivalent to the neglect of the displacement current.&lt;/p&gt;&lt;/abstract&gt;</p>

    DOI

    Scopus

  • Zakharov system in two space dimensions

    Tohru Ozawa, Kenta Tomioka

    Nonlinear Analysis   214   112532 - 112532  2022年01月  [査読有り]

    DOI

    Scopus

    5
    被引用数
    (Scopus)

  • A note on 2D Navier–Stokes equations

    Jishan Fan, Tohru Ozawa

    Partial Differential Equations and Applications   2 ( 6 )  2021年12月  [査読有り]

    　概要を見る

    <title>Abstract</title>In this note, we prove a new <inline-formula><alternatives><tex-math>$$L^4$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
    <mml:msup>
    <mml:mi>L</mml:mi>
    <mml:mn>4</mml:mn>
    </mml:msup>
    </mml:math></alternatives></inline-formula>-estimate of the velocity by the technique of Hardy space <inline-formula><alternatives><tex-math>$${\mathcal {H } }^1$$</tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
    <mml:msup>
    <mml:mrow>
    <mml:mi>H</mml:mi>
    </mml:mrow>
    <mml:mn>1</mml:mn>
    </mml:msup>
    </mml:math></alternatives></inline-formula> and <italic>BMO</italic>.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Regularity criteria for a Ginzburg-Landau-Navier-Stokes system

    J. Fan, T.Ozawa

    Funkcialaj Ekvacioj   64   349 - 360  2021年11月  [査読有り]

  • Small Data Scattering of Hartree Type Fractional Schrödinger Equations in a Scaling Critical Space

    Yonggeun Cho, Tohru Ozawa, Changhun Yang

    Funkcialaj Ekvacioj   64 ( 1 ) 1 - 15  2021年04月  [査読有り]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Uniform Regularity for a Compressible Gross-Pitaevskii-Navier-Stokes System

    Jishan Fan, Tohru Ozawa

    Nonlinear Partial Differential Equations for Future Applications   346   95 - 102  2021年04月  [査読有り]

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Poincaré inequalities with exact missing terms on homogeneous groups

    T. Ozawa, D. Suragan

    Journal of the Mathematical Society of Japan   73 ( 2 ) 497 - 503  2021年04月  [査読有り]

  • A note on bilinear estimates in the homogeneous Triebel-Lizorkin spaces

    J. Fan, T.Ozawa

    RIMS Kokyuroku Bessatsu   B88   147 - 150  2021年  [査読有り]

  • Well-posedness of a 2D time-dependent Ginzburg-Landau superconductivity model

    J. Fan, T. Ozawa

    Nonlinear Analysis and Differential Equations   8 ( 1 ) 89 - 97  2021年01月  [査読有り]

  • Sharp remainder of the Poincaré inequality

    T. Ozawa, D. Suragan

    Proceedings of the American Mathematical Society   148 ( 10 ) 4235 - 4239  2020年10月  [査読有り]

  • Global solutions to the Maxwell-Navier-Stokes system in a bounded domain in 2D

    J. Fan, T. Ozawa

    Zeitschrift für angewandte Mathematik und Physik   71 ( 136 )  2020年07月  [査読有り]

  • Existence and uniqueness of classical paths under quadratic potentials

    K. Narita, T. Ozawa

    Calculus of Variations and PDE's   59 ( 128 )  2020年07月  [査読有り]

  • Self-similar solutions to the derivative nonlinear Schrödinger equation

    K. Fujiwara, V. Georgiev, T. Ozawa

    Journal of Differential Equations   268 ( 12 ) 7940 - 7961  2020年06月  [査読有り]

  • Multidimensional inverse Cauchy problems for evolution equations

    M. Karazym, T.Ozawa, D. Suragan

    Inverse Problems in Science and Engineering   28 ( 11 ) 1582 - 1590  2020年05月  [査読有り]

  • A blow-up criterion for the modified Navier-Stokes-Fourier equations

    J. Fan, T. Ozawa

    Journal of Mathematical Fluid Mechanics   22, Article number 16  2020年02月  [査読有り]

  • Well-posedness for a generalized klein-gordon-Schrödinger equations

    Jishan Fan, Tohru Ozawa

    Trends in Mathematics     309 - 317  2020年

    　概要を見る

    We first prove uniform-in-ε regularity estimates of strong solutions to a generalized Klein-Gordon-Schrödinger equations in (formula presented). Here ε is the dispersion coefficient. Then we prove the global well-posedness of strong solutions to the limit problem (formula presented) when n ≤ 3.

    DOI

    Scopus

  • Cauchy problem and vanishing dispersion limit for Schr&ouml;dinger-improved Boussinesq equations

    J. Fan, T. Ozawa

    Journal of Mathematical Analysis and Applications   485, Issue 2   123857  2020年01月  [査読有り]

  • Hardy type inequalities with spherical derivatives

    N. Bez, S. Machihara, T. Ozawa

    SN Partial Differential Equations and Applications   1, Issue 1, Article 5.  2020年01月  [査読有り]

  • On global well-posedness for nonlinear semirelativistic equations in some scaling subcritical and critical cases

    K. Fujiwara, V. Georgiev, T. Ozawa

    J. Math. Pures Appl.,   136   239 - 256  2020年  [査読有り]

  • A note on bilinear estimates in the Sobolev spaces

    J. Fan, T. Ozawa

    International Journal of Mathematical Analysis   13 ( 12 ) 551 - 554  2019年11月  [査読有り]

    DOI

  • Remarks on the Hardy type inequalities with remainder terms in the framework of equalities

    S. Machihara, T. Ozawa, H. Wadade

    Adv. Studies Pure Math.   81   247 - 258  2019年11月  [査読有り]

  • Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential

    L. Forcella, K. Fujiwara, V. Georgiev, T. Ozawa

    Discrete and Continuous Dynamical Systems A   39 ( 5 ) 2661 - 2678  2019年05月  [査読有り]

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • Lp-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

    T. Ozawa, M. Ruzhansky, D. Suragan

    Quaterly J. Math.   70 ( 1 ) 305 - 318  2019年03月  [査読有り]

    DOI

    Scopus

    12
    被引用数
    (Scopus)

  • Blow-Up or Global Existence for the Fractional Ginzburg-Landau Equation in Multi-dimensional Case

    Luigi Forcella, Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

    Trends in Mathematics     179 - 202  2019年

    　概要を見る

    The aim of this work is to give a complete picture concerning the asymptotic behaviour of the solutions to fractional Ginzburg-Landau equation. In previous works, we have shown global well-posedness for the past interval in the case where spatial dimension is less than or equal to 3. Moreover, we have also shown blow-up of solutions for the future interval in one dimensional case. In this work, we summarise the asymptotic behaviour in the case where spatial dimension is less than or equal to 3 by proving blow-up of solutions for a future time interval in multidimensional case. The result is obtained via ODE argument by exploiting a new weighted commutator estimate.

    DOI

    Scopus

    2
    被引用数
    (Scopus)

  • Note for global existence of semilinear heat equation in weighted $L^\infty$ space

    K. Fujiwara, V. Georgiev, T. Ozawa

    Pliska Stud. Math.   30   7 - 20  2019年  [査読有り]

  • Dynamical behavior for the solutions of the Navier-Stokes equation

    Kuijie Li, Tohru Ozawa, Baoxiang Wang

    Communications on Pure and Applied Analysis   17 ( 4 ) 1511 - 1560  2018年07月  [査読有り]

    　概要を見る

    We study several quantitative properties of solutions to the incompressible Navier-Stokes equation in three and higher dimensions: (Equation Presented) More precisely, for the blow up mild solutions with initial data in L∞(ℝRd) and Hd/2-1(ℝd), we obtain a concentration phenomenon and blowup profile decomposition respectively. On the other hand, if the Fourier support has the form supp u0 ⊂ {ξ ∈ ℝn : ξ1 ≥ L} and ||u0||∞ ≪ L for some L &gt
    0, then (1) has a unique global solution u ∈ C(ℝR+
    L∞). In 3D, we show the compactness of the set consisting of minimal-Lp singularity-generating initial data with 3 &lt
    p &lt
    1, furthermore, if the mild solution with data in Lp(ℝ3) blows up in a Type-I manner, we prove the existence of a blowup solution which is uniformly bounded in critical Besov spaces B-1+6/p p/2,∞ (ℝ3).

    DOI

    Scopus

    11
    被引用数
    (Scopus)

  • Higher Order Fractional Leibniz Rule

    Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

    Journal of Fourier Analysis and Applications   24 ( 3 ) 650 - 665  2018年06月  [査読有り]

    　概要を見る

    The fractional Leibniz rule is generalized by the Coifman–Meyer estimate. It is shown that the arbitrary redistribution of fractional derivatives for higher order with the corresponding correction terms.

    DOI

    Scopus

    24
    被引用数
    (Scopus)

  • On the focusing energy-critical fractional nonlinear schrödnger equations

    Y. Cho, G. Hwang, T. Ozawa

    Advances in Differential Equations   23 ( 3-4 ) 161 - 192  2018年03月  [査読有り]

  • Global well-posedness of weak solutions to the time-dependent Ginzburg-Landau model for superconductivity

    J. Fan, T. Ozawa

    Taiwanese J. Math.   22 ( 4 ) 851 - 858  2018年  [査読有り]

    DOI

    Scopus

    18
    被引用数
    (Scopus)

  • Blow-up for self-interacting fractional Ginzburg-Landau equation

    Kazumasa Fujiwara, Vladimir Georgiev, Tohru Ozawa

    Dynamics of Partial Differential Equations   15 ( 3 ) 175 - 182  2018年  [査読有り]

    　概要を見る

    The blow-up of solutions for the Cauchy problem of fractional Ginzburg-Landau equation with non-positive nonlinearity is shown by an ODE argument. Moreover, in one dimensional case, the optimal lifespan estimate for size of initial data is obtained.

    DOI

    Scopus

    7
    被引用数
    (Scopus)

  • Lifespan of strong solutions to the periodic derivative nonlinear Schrödinger equation

    K. Fujiwara, T. Ozawa

    Evolution Equations and Control Theory   7 ( 2 ) 275 - 280  2018年  [査読有り]

    DOI

    Scopus

  • Small data scattering of Hartree type fractional Schrödinger equations in dimension 2 and 3

    Y. Cho, T. Ozawa

    J. Korean Math. Soc.   55 ( 2 ) 373 - 390  2018年  [査読有り]

    DOI

    Scopus

    3
    被引用数
    (Scopus)

  • Ground states for semi-relativistic Schrödinger-Poisson-Slater energy

    J. Bellazzini, T. Ozawa, N. Visciglia

    Funkcialaj Ekvacioj   60 ( 3 ) 353 - 369  2017年12月  [査読有り]

    DOI

    Scopus

    5
    被引用数
    (Scopus)

  • Hardy type inequalities in Lp with sharp remainders

    Norisuke Ioku, Michinori Ishiwata, Tohru Ozawa

    Journal of Inequalities and Applications   2017 ( 1 )  2017年12月  [査読有り]

    　概要を見る

    Sharp remainder terms are explicitly given on the standard Hardy inequalities in Lp(Rn) with 1 &lt
    p&lt
    n. Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals.

    DOI

    Scopus

    18
    被引用数
    (Scopus)

  • Lifespan of strong solutions to the periodic nonlinear Schrödinger equation without gauge invariance

    K. Fujiwara, T. Ozawa

    Journal of Evolution Equations   17 ( 3 ) 1023 - 1030  2017年09月  [査読有り]

    DOI

    Scopus

    10
    被引用数
    (Scopus)

  • Local well-posedness for an Ericksen-Leslie’s parabolic-hyperbolic compressible non-isothermal model for liquid crystals

    J. Fan, T. Ozawa

    Electronic Journal of Differential Equations   2017 ( 232 ) 1 - 8  2017年09月  [査読有り]

  • Remarks on the Rellich inequality

    Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    MATHEMATISCHE ZEITSCHRIFT   286 ( 3-4 ) 1367 - 1373  2017年08月  [査読有り]

    　概要を見る

    We study the Rellich inequalities in the framework of equalities. We present equalities which imply the Rellich inequalities by dropping remainders. This provides a simple and direct understanding of the Rellich inequalities as well as the nonexistence of nontrivial extremisers.

    DOI

    Scopus

    19
    被引用数
    (Scopus)

  • Short-range scattering of Hartree type fractional NLS II

    Yonggeun Cho, Tohru Ozawa

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   157   62 - 75  2017年07月  [査読有り]

    　概要を見る

    We prove the small data scattering for Hartree type fractional Schrodinger equation with inverse square potential. This is the border line problem between Strichartz range and weighted space range in view of the method of approach. To show this we carry out a subtle trilinear estimate via fractional Leibniz rule and Balakrishnan's formula. This paper is a sequel of the previous result (Cho, 2017). (C) 2017 Elsevier Ltd. All rights reserved.

    DOI

    Scopus

    6
    被引用数
    (Scopus)

  • Stability of Trace Theorems on the Sphere

    Neal Bez, Chris Jeavons, Tohru Ozawa, Mitsuru Sugimoto

    Journal of Geometric Analysis   28   1 - 21  2017年06月  [査読有り]

    　概要を見る

    We prove stable versions of trace theorems on the sphere in (Formula presented.) with optimal constants, thus obtaining rather precise information regarding near-extremisers. We also obtain stability for the trace theorem into (Formula presented.) for (Formula presented.), by combining a refined Hardy–Littlewood–Sobolev inequality on the sphere with a duality–stability result proved very recently by Carlen. Finally, we extend a local version of Carlen’s duality theorem to establish local stability of certain Strichartz estimates for the kinetic transport equation.

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • ON LANDAU-KOLMOGOROV INEQUALITIES FOR DISSIPATIVE OPERATORS

    Masayuki Hayashi, Tohru Ozawa

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   145 ( 2 ) 847 - 852  2017年02月  [査読有り]

    　概要を見る

    We revisit Kato's theory on Landau-Kolmogorov (or Kallman-Rota) inequalities for dissipative operators in an algebraic framework in a scalar product space.

    DOI

    Scopus

    6
    被引用数
    (Scopus)

  • Hardy type inequalities in L-p with sharp remainders

    Norisuke Ioku, Michinori Ishiwata, Tohru Ozawa

    JOURNAL OF INEQUALITIES AND APPLICATIONS    2017年01月  [査読有り]

    　概要を見る

    Sharp remainder terms are explicitly given on the standard Hardy inequalities in L-p(R-n) with 1 &lt; p &lt; n. Those remainder terms provide a direct and exact understanding of Hardy type inequalities in the framework of equalities as well as of the nonexistence of nontrivial extremals.

    DOI

    Scopus

    18
    被引用数
    (Scopus)

  • A note on regularity criteria for Navier-Stokes system: Note on Navier-Stokes

    Jishan Fan, Tohru Ozawa

    Springer Proceedings in Mathematics and Statistics   215   47 - 50  2017年  [査読有り]

    　概要を見る

    We use some interpolation inequalities on Besov spaces to show a regularity criterion for n-dimensional Navier-Stokes system.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Uniform regularity for the time-dependent Ginzburg-Landau-Maxwell equations

    J. Fan, T. Ozawa

    “New Trends in Analysis and Interdisciplinary Applications,” Trends in Mathematics, Springer     301 - 306  2017年  [査読有り]

  • A conjecture regarding optimal Strichartz estimates for the wave equation

    N. Bez, C. Jeavons, T. Ozawa, H. Saito

    “New Trends in Analysis and Interdisciplinary Applications,” Trends in Mathematics, Springer     293 - 300  2017年  [査読有り]

  • Weak solutions to the time-dependent Ginzburg-Landau-Maxwell equations

    J. Fan, T. Ozawa

    RIMS Kokyuroku Bessatsu   63   23 - 30  2017年  [査読有り]

  • Uniform existence and uniqueness for a time-dependent Ginzburg-Landau model for superconductivity

    J. Fan, T. Ozawa

    Nonlinear Analysis and Differential Equations   5 ( 6 ) 249 - 259  2017年  [査読有り]

    DOI

  • Global well-posedness of weak solutions to the time-dependent Ginzburg-Landau model for superconductivity in R2

    J. Fan, T. Ozawa

    International Journal of Mathematical Analysis   11 ( 4 ) 199 - 207  2017年  [査読有り]

    DOI

  • REGULARITY CRITERIA FOR NAVIER-STOKES AND RELATED SYSTEM

    Jishan Fan, Tohru Ozawa

    DIFFERENTIAL AND INTEGRAL EQUATIONS   30 ( 1-2 ) 101 - 114  2017年01月  [査読有り]

    　概要を見る

    We show some regularity criteria for Navier-Stokes equations, the harmonic heat flow, two liquid crystals models, and a model for magneto-elastic materials. The method of proof depends on a systematic use of interpolation inequalities in Besov spaces and is independent on logarithmic inequalities.

  • Uncertainty relations in the framework of equalities

    Tohru Ozawa, Kazuya Yuasa

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   445 ( 1 ) 998 - 1012  2017年01月  [査読有り]

    　概要を見る

    We study the Schrodinger Robertson uncertainty relations in an algebraic framework. Moreover, we show that some specific commutation relations imply new equalities, which are regarded as equality versions of well-known inequalities such as Hardy's inequality. (C) 2016 Elsevier Inc. All rights reserved.

    DOI

    Scopus

    6
    被引用数
    (Scopus)

  • Well-posedness for a generalized derivative nonlinear Schrödinger equation

    M. Hayashi, T. Ozawa

    J.Differential Equations   261 ( 10 ) 5424 - 5445  2016年11月  [査読有り]

    DOI

    Scopus

    37
    被引用数
    (Scopus)

  • ON SMALL DATA SCATTERING OF HARTREE EQUATIONS WITH SHORT-RANGE INTERACTION

    Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa

    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS   15 ( 5 ) 1809 - 1823  2016年09月  [査読有り]

    　概要を見る

    In this note we study Hartree type equations with vertical bar del vertical bar(alpha) (1 &lt; alpha &lt;= 2) and potential whose Fourier transform behaves like vertical bar gamma vertical bar(-(d-gamma 1)) at the origin and vertical bar xi vertical bar(-(d-gamma 1)) at infinity. We show non-existence of scattering when 0 &lt; gamma(1) &lt;= 1 and small data scattering in H-S for s &gt; 2 2-alpha/2 when 2 &lt; gamma(1) &lt;= d and 0 &lt; gamma(2) &lt;= 2. For this we use U-P-V-P space argument and Strichartz estimates.

    DOI

    Scopus

    9
    被引用数
    (Scopus)

  • Finite time blowup of solutions to the nonlinear Schrödinger equation without gauge invariance

    K. Fujiwara, T. Ozawa

    Journal of Mathematical Physics   57 ( 8 )  2016年08月  [査読有り]

    DOI

    Scopus

    13
    被引用数
    (Scopus)

  • Normal form and global solutions for the Klein-Gordon-Zakharov equations

    T. Ozawa, K. Tsutaya, Y. Tsutsumi

    Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire   12 ( 4 ) 459 - 503  2016年07月  [査読有り]

    　概要を見る

    In this paper we study the global existence and asymptotic behavior of solutions for the Cauchy problem of the Klein-Gordon-Zakharov equations in three space dimensions. We prove that for small initial data, there exist the unique global solutions of the Klein-Gordon-Zakharov equations. We also show that these solutions approach asymptotically the free solutions as t → ∞. Our proof is based on the method of normal forms introduced by Shatah [12], which transforms the original system with quadratic nonlinearity into a new system with cubic nonlinearity.

    DOI

    Scopus

    53
    被引用数
    (Scopus)

  • An improvement on the Brézis–Gallouët technique for 2D NLS and 1D half-wave equation

    T. Ozawa, N. Visciglia

    Ann. Inst. Henri Poincaré, Analyse non linéaire   33 ( 4 ) 1069 - 1079  2016年07月  [査読有り]

    DOI

    Scopus

    20
    被引用数
    (Scopus)

  • Space-time analytic smoothing effect for the pseudo-conformally invariant Schrödinger equations

    G. Hoshino, T. Ozawa

    Nonlinear Differential Equations and Applications   23 ( 1 ) 1 - 10  2016年02月  [査読有り]

    DOI

    Scopus

    5
    被引用数
    (Scopus)

  • Remarks on bilinear estimates in the Sobolev spaces

    K. Fujiwara, T. Ozawa

    RIMS Kokyuroku Bessatsu   56   1 - 9  2016年  [査読有り]

    CiNii

  • Blow-up criterion for 3D navier-stokes equations and Landau-Lifshitz system in a bounded domain

    Jishan Fan, Tohru Ozawa

    Advances in Mathematical Fluid Mechanics - Dedicated to Giovanni Paolo Galdi on the Occasion of His 60th Birthday   none   175 - 182  2016年  [査読有り]

    　概要を見る

    In this paper we prove a blow-up criterion for the 3D Navier-Stokes equations in a bounded domain in terms of a BMO norm of vorticity. We will also prove a regularity criterion for the Landau-Lifshitz system in a bounded domain.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Some remarks on gauge choice and Navier-Stokes equations

    J. Fan, T. Ozawa

    Nonlinear Analysis and Differential Equations   4 ( 14 ) 659 - 667  2016年  [査読有り]

    DOI

  • Global strong solutions to the time-dependent Ginzburg-Landau model in superconductivity with four new gauges

    J. Fan, T. Ozawa

    Nonlinear Analysis and Differential Equations   4 ( 11 ) 513 - 519  2016年  [査読有り]

    DOI

  • Remarks on regularity criteria for harmonic heat flow and related system

    Jishan Fan, Tohru Ozawa

    International Journal of Mathematical Analysis   10 ( 13-16 ) 749 - 755  2016年  [査読有り]

    　概要を見る

    We prove regularity criteria for harmonic heat flow and a liquid crystals model.

    DOI

    Scopus

  • Weighted L-P-boundedness of convolution type integral operators associated with bilinear estimates in the Sobolev spaces

    Kazumasa Fujiwara, Tohru Ozawa

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   68 ( 1 ) 169 - 191  2016年01月  [査読有り]

    DOI CiNii

    Scopus

    1
    被引用数
    (Scopus)

  • Sharp lower bounds for Coulomb energy

    Jacopo Bellazzini, Marco Ghimenti, Tohru Ozawa

    MATHEMATICAL RESEARCH LETTERS   23 ( 3 ) 621 - 632  2016年  [査読有り]

    　概要を見る

    We prove L-p lower bounds for Coulomb energy for radially symmetric functions in H(over dot)(s)(R-3) with 1/2 &lt; s &lt; 3/2. In case 1/2 &lt; s &lt;= 1 we show that the lower bounds are sharp.

    DOI

    Scopus

    13
    被引用数
    (Scopus)

  • FINITE TIME BLOWUP FOR THE FOURTH-ORDER NLS

    Yonggeun Cho, Tohru Ozawa, Chengbo Wang

    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY   53 ( 2 ) 615 - 640  2016年  [査読有り]

    　概要を見る

    We consider the fourth-order Schrodinger equation with focusing inhomogeneous nonlinearity (-vertical bar x vertical bar(-2)vertical bar u vertical bar(4/n) u) in high space dimensions. Extending Glassey's virial argument, we show the finite time blow-up of solutions when the energy is negative.

    DOI

    Scopus

    19
    被引用数
    (Scopus)

  • SOME SHARP BILINEAR SPACE-TIME ESTIMATES FOR THE WAVE EQUATION

    Neal Bez, Chris Jeavons, Tohru Ozawa

    MATHEMATIKA   62 ( 3 ) 719 - 737  2016年  [査読有り]

    　概要を見る

    We prove a family of sharp bilinear space-time estimates for the halfwave propagator e(it root-Delta). As a consequence, for radially symmetric initial data, we establish sharp estimates of this kind for a range of exponents beyond the classical range.

    DOI

    Scopus

    8
    被引用数
    (Scopus)

  • ANALYTIC SMOOTHING EFFECT FOR THE CUBIC HYPERBOLIC SCHRODINGER EQUATION IN TWO SPACE DIMENSIONS

    Gaku Hoshino, Tohru Ozawa

    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS   2016   1 - 8  2016年01月  [査読有り]

    　概要を見る

    We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.

  • Regularity criteria for harmonic heat flow and related system

    Jishan Fan, Tohru Ozawa

    MATHEMATISCHE NACHRICHTEN   289 ( 1 ) 28 - 33  2016年01月  [査読有り]

    　概要を見る

    We will prove some regularity criteria for harmonic heat flow, biharmonic heat flow and a surface growth model. (C) 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Sharp remainder of a critical Hardy inequality

    Norisuke Ioku, Michinori Ishiwata, Tohru Ozawa

    ARCHIV DER MATHEMATIK   106 ( 1 ) 65 - 71  2016年01月  [査読有り]

    　概要を見る

    An explicit representation is given to the remainder of a critical Hardy inequality in L-n (R-n) with n &gt;= 2.

    DOI

    Scopus

    40
    被引用数
    (Scopus)

  • Weak solutions to the Ginzburg-Landau model in superconductivity with the temporal gauge

    Jishan Fan, Tohru Ozawa

    APPLICABLE ANALYSIS   95 ( 9 ) 2029 - 2038  2016年  [査読有り]

    　概要を見る

    We first prove the uniqueness of weak solutions (psi, A) to the 3-D Ginzburg-Landau system in superconductivity with the temporal gauge if (psi, A). W := {(psi, A)vertical bar psi is an element of L-2(0, T; L-infinity), del psi is an element of L-2(0, T; L-3), A is an element of C([0, T]; L-3)}, which is a critical space for some positive constant T. We also prove the global existence of solutions for the Ginzburg-Landau system with magnetic diffusivity mu &gt; 0 or mu = 0. Finally, we prove the uniform bounds with respect to mu of strong solutions in space dimensions d = 2. Consequently, the existence of the limit as mu -&gt; 0 can be established.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

    Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    Journal of Inequalities and Applications   2015 ( 1 )  2015年12月  [査読有り]

    　概要を見る

    In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in R&lt
    sup&gt
    n&lt
    /sup&gt
    in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.

    DOI

    Scopus

    14
    被引用数
    (Scopus)

  • Scaling invariant Hardy inequalities of multiple logarithmic type on the whole space

    Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    JOURNAL OF INEQUALITIES AND APPLICATIONS    2015年09月  [査読有り]

    　概要を見る

    In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in R-n in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.

    DOI

    Scopus

    14
    被引用数
    (Scopus)

  • Well-Posedness for the Cauchy Problem for a System of Semirelativistic Equations

    Kazumasa Fujiwara, Shuji Machihara, Tohru Ozawa

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   338 ( 1 ) 367 - 391  2015年08月  [査読有り]

    　概要を見る

    The local well-posedness for the Cauchy problem of a system of semirelativistic equations in one space dimension is shown in the Sobolev space H-s of order s &gt;= 0. We apply the standard contraction mapping theorem by using Bourgain type spaces X-s,X-b. We also use an auxiliary space for the solution in L-2 = H-0. We give the global well-posedness by this conservation law and the argument of the persistence of regularity.

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • ON A SYSTEM OF SEMIRELATIVISTIC EQUATIONS IN THE ENERGY SPACE

    Kazumasa Fujiwara, Shuji Machihara, Tohru Ozawa

    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS   14 ( 4 ) 1343 - 1355  2015年07月  [査読有り]

    　概要を見る

    Well-posedness of the Cauchy problem for a system of semirelativistic equations is shown in the energy space. Solutions are constructed as a limit of an approximate solutions. A Yudovitch type argument plays an important role for the convergence arguments.

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • Analytic smoothing effect for a system of Schrödinger equations with two wave interaction

    G. Hoshino, T. Ozawa

    Adv. Differential Equations   20 ( 7-8 ) 697 - 716  2015年07月  [査読有り]

  • Finite time extinction for nonlinear Schrödinger equation in 1D and 2D

    R. Carles, T. Ozawa

    Commun. PDE.   40 ( 5 ) 897 - 917  2015年05月  [査読有り]

    DOI

    Scopus

    14
    被引用数
    (Scopus)

  • Remark on a semirelativistic equation in the energy space

    K. Fujiwara, S. Machihara, T. Ozawa

    Discrete and Continuous Dynamical Systems, Suppl.     473 - 478  2015年  [査読有り]

    DOI

  • A regularity criterion for 3D density-dependent MHD system with zero viscocity

    J. Fan, T. Ozawa

    Discrete and Continuous Dynamical Systems, Suppl.     395 - 399  2015年  [査読有り]

    DOI

  • A regularity criterion for the Schrödinger map

    J. Fan, T. Ozawa

    “Current Trends in Analysis and Its Applications,” Trends in Mathematics, Springer   2   217 - 223  2015年  [査読有り]

    DOI

  • Remarks on global solutions to the cauchy problem for semirelativistic equations with power type nonlinearity

    Kazumasa Fujiwara, Tohru Ozawa

    International Journal of Mathematical Analysis   9 ( 53-56 ) 2599 - 2610  2015年  [査読有り]

    　概要を見る

    Existence and nonexistence results on global solutions to the Cauchy problem for semirelativistic equations are shown by a simple compact- ness argument and a test function method, respectively. To obtain the nonexistence of global solutions, semirelativistic equations are trans- formed into a new equation without nonlocal operators in linear part but with a time derivative in nonlinear part, which is shown to be under control of special choice of test functions.

    DOI

    Scopus

    10
    被引用数
    (Scopus)

  • Analytic smoothing effect for a system of Schrödinger equations with three wave interaction

    G. Hoshino, T. Ozawa

    Journal of Mathematical Physics   56 ( 9 )  2015年  [査読有り]

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • Regularity criteria for the incompressible MHD with the hall or ion-slip effects

    Jishan Fan, Tohru Ozawa

    International Journal of Mathematical Analysis   9 ( 21-24 ) 1173 - 1186  2015年  [査読有り]

    　概要を見る

    This paper proves some regularity criteria for the 3D incompressible MHD with the Hall or ion-slip effects.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • On the semilinear Schrödinger equation with time dependent coefficients

    T. Gonda, S. Machihara, T. Ozawa

    Math. Nachr.   287 ( 17-18 ) 1986 - 2001  2014年12月  [査読有り]

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • Analytic smoothing effect for nonlinear Schrödinger equation with quintic nonlinearity

    G. Hoshino, T. Ozawa

    J. Math. Anal. Appl.   419 ( 1 ) 285 - 297  2014年11月  [査読有り]

    DOI

    Scopus

    26
    被引用数
    (Scopus)

  • Regularity criteria for the density-dependent Hall-magnetohydrodynamics

    Jishan Fan, Tohru Ozawa

    APPLIED MATHEMATICS LETTERS   36   14 - 18  2014年10月  [査読有り]

    　概要を見る

    This paper proves two regularity criteria for the density-dependent Hall-MHD system with positive initial density. We also prove a global nonexistence result for initial density with a high decrease at infinity. (C) 2014 Elsevier Ltd. All rights reserved.

    DOI

    Scopus

    14
    被引用数
    (Scopus)

  • Notes on the paper entitled 'Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces'

    Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2014:253  2014年07月  [査読有り]

    DOI

    Scopus

  • ANALYTIC SMOOTHING EFFECT FOR NONLINEAR SCHRODINGER EQUATION IN TWO SPACE DIMENSIONS

    Gaku Hoshino, Tohru Ozawa

    OSAKA JOURNAL OF MATHEMATICS   51 ( 3 ) 609 - 618  2014年07月  [査読有り]

    　概要を見る

    We prove the global existence of analytic solutions to the Cauchy problem for nonlinear Schrodinger equations in two dimensions, where the nonlinearity behaves as a cubic power at the origin and the Cauchy data are small and decay exponentially at infinity.

  • Stability of the Young and Hölder inequalities

    K. Fujiwara, T. Ozawa

    J. Ineq. Appl.   2014:162  2014年05月  [査読有り]

    DOI

    Scopus

    5
    被引用数
    (Scopus)

  • On the orbital stability of fractional Schrödinger equations

    Y. Cho, H. Hajaiej, G. Hwang, T. Ozawa

    Commun. Pure Appl. Anal.   13 ( 3 ) 1267 - 1282  2014年05月  [査読有り]

    DOI

    Scopus

    44
    被引用数
    (Scopus)

  • REGULARITY CRITERIA FOR THE 2D MHD SYSTEM WITH HORIZONTAL DISSIPATION AND HORIZONTAL MAGNETIC DIFFUSION

    Jishan Fan, Tohru Ozawa

    KINETIC AND RELATED MODELS   7 ( 1 ) 45 - 56  2014年03月  [査読有り]

    　概要を見る

    This paper proves some regularity criteria for the 2D MHD system with horizontal dissipation and horizontal magnetic diffusion. We also prove the global existence of strong solutions of its regularized MHD-alpha system.

    DOI

    Scopus

    14
    被引用数
    (Scopus)

  • On the Hardy type inequality in critical Sobolev-Lorentz spaces

    S. Machihara, T. Ozawa, H. Wadade

    RIMS Kokyuroku Bessatsu   49   103 - 118  2014年  [査読有り]

    　概要を見る

    "Harmonic Analysis and Nonlinear Partial Differential Equations". July 8～10, 2013. edited by Mitsuru Sugimoto and Hideo Kubo. The papers presented in this volume of RIMS Kokyuroku Bessatsu are in final form and refereed.

    CiNii

  • Analytic smoothing effect for nonlinear Schrödinger equations with quadratic interaction

    G. Hoshino, T. Ozawa

    RIMS Kokyuroku Bessatsu   49   1 - 12  2014年  [査読有り]

    　概要を見る

    "Harmonic Analysis and Nonlinear Partial Differential Equations". July 8～10, 2013. edited by Mitsuru Sugimoto and Hideo Kubo. The papers presented in this volume of RIMS Kokyuroku Bessatsu are in final form and refereed.

    CiNii

  • Regularity criteria for Hall-magnetohydrodynamics and the space-time Monopole equation in Lorenz gauge

    Jishan Fan, Tohru Ozawa

    HARMONIC ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS   612   81 - +  2014年  [査読有り]

    　概要を見る

    We prove some regularity criteria of local smooth solutions for viscous or inviscid Hall-MHD model and the space-time Monopole equation in the Lorenz gauge. We also prove time decay estimates for weak solutions of the viscous Hall-MHD model by the Fourier splitting device.

    DOI

  • Uniform regularity for the Landau-Lifshitz-Maxwell system without Dissipation

    Jishan Fan, Tohru Ozawa

    Applied Mathematical Sciences   8 ( 169-172 ) 8547 - 8557  2014年  [査読有り]

    　概要を見る

    In this paper, we prove the existence of local solutions to the Cauchy problem for the 3D Landau-Lifshitz-Maxwell system without dissipation, where the local existence time and the corresponding Sobolev estimates are independent of the dielectric constant e{open} with 0 &lt
    ε &lt
    1. Consequently, the limit as ε → 0 can be established.

    DOI

    Scopus

  • Identities for the difference between the arithmetic and geometric means

    Kazumasa Fujiwara, Tohru Ozawa

    International Journal of Mathematical Analysis   8 ( 29-32 ) 1525 - 1542  2014年  [査読有り]

    　概要を見る

    We prove a formula which expresses the difference between the arithmetic mean of variables of odd numbers and the corresponding geometric mean in the form of a linear combination of independent variables with coefficients given by sums of squares of polynomials.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • A Sharp Bilinear Estimate for the Klein-Gordon Equation in R1+1

    Tohru Ozawa, Keith M. Rogers

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   ( 5 ) 1367 - 1378  2014年  [査読有り]

    　概要を見る

    We prove a sharp bilinear estimate for the one-dimensional Klein-Gordon equation. The proof involves an unlikely combination of five trigonometric identities. We also prove new estimates for the restriction of the Fourier transform to the hyperbola, where the pullback measure is not assumed to be compactly supported.

    DOI

    Scopus

    10
    被引用数
    (Scopus)

  • A blow-up criterion for the 3d full magnetohydrodynamic equations

    Jishan Fan, Tohru Ozawa

    International Journal of Mathematical Analysis   8 ( 1-4 ) 101 - 108  2014年  [査読有り]

    　概要を見る

    In this paper we establish a regularity criterion for the 3D incompressible full MHD equations with variable viscosity. © 2014 Jishan Fan and Tohru Ozawa.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Global existence of strong solutions to a time-dependent 3D Ginzburg-Landau model for superconductivity with partial viscous terms

    Jishan Fan, Tohru Ozawa

    MATHEMATISCHE NACHRICHTEN   286 ( 17-18 ) 1792 - 1796  2013年12月  [査読有り]

    　概要を見る

    We study an initial boundary value problem for a time-dependent 3D Ginzburg-Landau model of superconductivity with partial viscous terms. We prove the global existence of strong solutions. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Generalizations of the logarithmic Hardy inequality in critical Sobolev-Lorentz spaces

    Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    Journal of Inequalities and Applications   2013  2013年12月  [査読有り]

    　概要を見る

    In this paper, we establish the Hardy inequality of the logarithmic type in the critical Sobolev-Lorentz spaces. More precisely, we generalize the Hardy type inequality obtained in Edmunds and Triebel (Math. Nachr. 207:79-92, 1999). The generalized inequality allows us to take the exponents appearing in the inequality more flexibly, and its optimality is discussed in detail. O'Neil's inequality and its reverse play an essential role for the proof. © 2013 Machihara et al.
    licensee Springer.

    DOI

    Scopus

    9
    被引用数
    (Scopus)

  • SHARP MORAWETZ ESTIMATES

    Tohru Ozawa, Keith M. Rogers

    JOURNAL D ANALYSE MATHEMATIQUE   121   163 - 175  2013年10月  [査読有り]

    　概要を見る

    We prove sharp Morawetz estimates - global in time with a singular weight in the spatial variables - for the linear wave, Klein-Gordon, and Schrodinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.

    DOI

    Scopus

    22
    被引用数
    (Scopus)

  • HARDY TYPE INEQUALITIES ON BALLS

    Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

    TOHOKU MATHEMATICAL JOURNAL   65 ( 3 ) 321 - 330  2013年09月  [査読有り]

    　概要を見る

    Hardy type inequalities are presented on balls with radius R at the origin in R-n with n = 2 at least. A special attention is paid on the behavior of functions on the boundary.

  • On the Cauchy problem of fractional Schrödinger equation with Hartree type nonlinearity

    Y. Cho, H. Hajaiej, G. Hwang, T. Ozawa

    Funkcialaj Ekvacioj   56 ( 2 ) 193 - 224  2013年08月  [査読有り]

  • On a system of nonlinear Schrodinger equations with quadratic interaction

    Nakao Hayashi, Tohru Ozawa, Kazunaga Tanaka

    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE   30 ( 4 ) 661 - 690  2013年07月  [査読有り]

    　概要を見る

    We study a system of nonlinear Schrodinger equations with quadratic interaction in space dimension n &lt;= 6. The Cauchy problem is studied in L-2, in H-1, and in the weighted L-2 space &lt; x &gt; L--1(2) = F(H-1) under mass resonance condition, where &lt; x &gt; = (1 + vertical bar x vertical bar(2))(1/2) and F is the Fourier transform. The existence of ground states is studied by variational methods. Blow-up solutions are presented in an explicit form in terms of ground states under mass resonance condition, which ensures the invariance of the system under pseudo-conformal transformations. (c) 2012 Elsevier Masson SAS. All rights reserved.

    DOI

    Scopus

    69
    被引用数
    (Scopus)

  • Global well-posedness of critical nonlinear Schrödinger equations below L2

    Y. Cho, G. Hwang, T. Ozawa

    Discrete and Continuous Dynamical Systems A   33 ( 4 ) 1389 - 1405  2013年04月  [査読有り]

    DOI

    Scopus

    12
    被引用数
    (Scopus)

  • Small data blow-up for a system of nonlinear Schrödinger equations

    T. Ozawa, H. Sunagawa

    J. Math. Anal. Appl.   399 ( 1 ) 147 - 155  2013年03月  [査読有り]

    DOI

    Scopus

    22
    被引用数
    (Scopus)

  • FINITE CHARGE SOLUTIONS TO CUBIC SCHRODINGER EQUATIONS WITH A NONLOCAL NONLINEARITY IN ONE SPACE DIMENSION

    Kei Nakamura, Tohru Ozawa

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   33 ( 2 ) 789 - 801  2013年02月  [査読有り]

    　概要を見る

    We study the Cauchy problem for cubic Schrodinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L-2(R) without any approximating arguments.

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • A regularity criterion for compressible nematic liquid crystal flows

    J. Fan, T. Ozawa

    ISRN Mathematical Analysis   2013(2013), Article ID 271324, 4pages  2013年  [査読有り]

    DOI

  • An approximation model for the density-dependent magnetohydrodynamic equations

    J. Fan, T. Ozawa

    Discrete and Continuous Dynamical Systems, Suppl.     207 - 216  2013年  [査読有り]

  • Exact remainder formula for the young inequality and applications

    Kazumasa Fujiwara, Tohru Ozawa

    International Journal of Mathematical Analysis   7 ( 53-56 ) 2723 - 2735  2013年  [査読有り]

    　概要を見る

    We present explicit formulae for the remainder arising in the Young, Hölder, and Clarkson inequalities. © 2013 Kazumasa Fujiwara and Tohru Ozawa.

    DOI

    Scopus

    4
    被引用数
    (Scopus)

  • Analytic smoothing effect for a system of nonlinear Schr&#246;dinger equations

    G. Hoshino, T. Ozawa

    Differential Equations and Applications - DEA   5   395 - 408  2013年  [査読有り]

  • Some inequalities related to the lorentz spaces

    Shuji Machihara, Tohru Ozawa

    Hokkaido Mathematical Journal   42 ( 2 ) 247 - 267  2013年  [査読有り]

    　概要を見る

    In this paper we introduce three types of inequalities related to the Lorentz spaces on a measure space (M
    m).

    DOI

    Scopus

    1
    被引用数
    (Scopus)

  • Regularity criteria for a coupled Navier-Stokes and Q-tensor system

    J. Fan, T. Ozawa

    International Journal of Analysis   2013(2013), Article ID 718173, 5pages  2013年  [査読有り]

    DOI

  • A note on the existence of a ground state solution to a fractional Schrödinger equation

    Y. Cho, T. Ozawa

    Kyushu J. Math.   67 ( 1 ) 227 - 236  2013年  [査読有り]

    　概要を見る

    In this paper we show the existence of a non-trivial solution to a fractional Schrödinger equation, which turns out to be a global minimizer of a variational problem. We give a sharp condition for the existence of global minimizers. To do this we develop a new compactification scheme of angularly regular solutions.

    DOI CiNii

    Scopus

    3
    被引用数
    (Scopus)

  • A note on the null condition for quadratic nonlinear Klein-Gordon systems in two space dimensions

    Soichiro Katayama, Tohru Ozawa, Hideaki Sunagawa

    COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS   65 ( 9 ) 1285 - 1302  2012年09月  [査読有り]

    　概要を見る

    We consider the Cauchy problem for quadratic nonlinear Klein-Gordon systems in two space dimensions with masses satisfying the resonance relation. Under the null condition in the sense of J.-M. Delort, D. Fang, and R. Xue (J. Funct. Anal. 211 (2004), no. 2, 288323), we show the global existence of asymptotically free solutions if the initial data are sufficiently small in some weighted Sobolev space. Our proof is based on an algebraic characterization of nonlinearities satisfying the null condition. (c) 2012 Wiley Periodicals, Inc.

    DOI

    Scopus

    19
    被引用数
    (Scopus)

  • Uniqueness of weak solutions to the Ginzburg-Landau model for superconductivity

    Jishan Fan, Tohru Ozawa

    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK   63 ( 3 ) 453 - 459  2012年06月  [査読有り]

    　概要を見る

    We prove the uniqueness for weak solutions of the time-dependent 2-D Ginzburg-Landau model for superconductivity with L (2) initial data in the case of Coulomb gauge. This question was left open in Tang and Wang (Physica D, 88:139-166, 1995). We also prove the uniqueness of the 3-D radially symmetric solution in bounded annular domain with the choice of Lorentz gauge and L (2) initial data.

    DOI

    Scopus

    15
    被引用数
    (Scopus)

  • Regularity criteria for hyperbolic Navier-Stokes and related system

    J. Fan, T. Ozawa

    ISRN Mathematical Analysis   2012(2012), Article ID 796368, 7pages  2012年  [査読有り]

    DOI

  • Global strong solutions of the time-dependent Ginzburg-Landau model for superconductivity with a new gauge

    J. Fan, T. Ozawa

    International Journal of Mathematical Analysis   6   1679 - 1684  2012年  [査読有り]

  • Continuation criterion for the 2D liquid crystal flows

    J. Fan, T. Ozawa

    ISRN Mathematical Analysis   2012(2012), Article ID 248473, 7pages  2012年  [査読有り]

    DOI

  • Uniqueness of weak solutions to the 3D Ginzburg-Landau model for superconductivity

    J. Fan, T. Ozawa

    International Journal of Mathematical Analysis   6   1095 - 1104  2012年  [査読有り]

  • LOCAL CAUCHY PROBLEM FOR THE MHD EQUATIONS WITH MASS DIFFUSION

    Jishan Fan, Tohru Ozawa

    DIFFERENTIAL AND INTEGRAL EQUATIONS   24 ( 11-12 ) 1037 - 1046  2011年11月  [査読有り]

    　概要を見る

    This paper studies the Cauchy problem for the MHD equations with mass diffusion in a bounded domain in R(3). We use Tikhonov&apos;s fixed-point theorem to prove the existence and uniqueness of local solutions.

  • Invariant elliptic estimates

    Yonggeun Cho, Tohru Ozawa, Yong-Sun Shim

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   382 ( 1 ) 162 - 171  2011年10月  [査読有り]

    　概要を見る

    In this paper, we revisit elliptic estimates invariant under domain expansion. We improve the invariant elliptic estimates in the previous paper [Y. Cho, T. Ozawa, Y. Shim, Calc. Var. PDE 34 (2009) 321-339] via gradient estimate and discuss an application to the Lame system. (C) 2011 Elsevier Inc. All rights reserved.

    DOI

    Scopus

  • Global Cauchy problem of an ideal density-dependent MHD-α model

    J. Fan, T. Ozawa

    Discrete and Continuous Dynamical Systems, Suppl.   31   400 - 409  2011年09月  [査読有り]

  • Life span of positive solutions for a semilinear heat equation with general non-decaying initial data

    Tohru Ozawa, Yusuke Yamauchi

    Journal of Mathematical Analysis and Applications   379 ( 2 ) 518 - 523  2011年07月  [査読有り]

    　概要を見る

    We prove upper bounds on the life span of positive solutions for a semilinear heat equation. For non-decaying initial data, it is well known that the solutions blow up in finite time. We give two types estimates of the life span in terms of the limiting values of the initial data in space. © 2011 Elsevier Inc.

    DOI

    Scopus

    8
    被引用数
    (Scopus)

  • REMARKS ON SOME DISPERSIVE ESTIMATES

    Yonggeun Cho, Tohru Ozawa, Suxia Xia

    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS   10 ( 4 ) 1121 - 1128  2011年07月  [査読有り]

    　概要を見る

    In this paper we consider the initial value problem for i partial derivative(t)u + omega(vertical bar del vertical bar)u = 0. Under suitable smoothness and growth conditions on omega, we derive dispersive estimates which is the generalization of time decay and Strichartz estimates. We unify and also simplify dispersive estimates by utilizing the Bessel function. Another main ingredient of this paper is to revisit oscillatory integrals of [2].

    DOI

    Scopus

    72
    被引用数
    (Scopus)

  • On Hartree equations with derivatives

    Yonggeun Cho, Sanghyuk Lee, Tohru Ozawa

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   74 ( 6 ) 2094 - 2108  2011年03月  [査読有り]

    　概要を見る

    We consider the Cauchy problem of two types of Hartree equations with exchange-correlation correction terms:
    {iu(t) - Delta u = V(k)(u)u in R(1+n), k = 1, 2,
    u(0) = phi in R(n), n &gt;= 1,
    where
    V(1)(u) = vertical bar x vertical bar(-gamma) * (lambda(1)vertical bar u vertical bar(2) + lambda(2)vertical bar del u vertical bar(2)), V(2)(u) = vertical bar x vertical bar(-gamma) * (lambda vertical bar vertical bar del vertical bar(delta) u vertical bar(2)).
    We establish the well- posedness of Cauchy problems and show the smoothing effect of solutions for each 0 &lt; gamma &lt; n and 0 &lt;= delta &lt;= 1. (C) 2010 Elsevier Ltd. All rights reserved.

    DOI

    Scopus

    6
    被引用数
    (Scopus)

  • Necessary and sufficient conditions for the fractional Gagliardo-Nirenberg inequalities and applications to Navier- Stokes and generalized Boson equations

    H. Hajaiej, L. Molinet, T. Ozawa, B. Wang

    RIMS Kokyuroku Bessatsu   26   159 - 175  2011年  [査読有り]

    CiNii

  • Small data scattering for a system of nonlinear Schr&#246;dinger equations

    N. Hayashi, C. Li, T. Ozawa

    Differential Equations and Applications - DEA   3   415 - 426  2011年  [査読有り]

  • REGULARITY CRITERION FOR THE INCOMPRESSIBLE VISCOELASTIC FLUID SYSTEM

    Jishan Fan, Tohru Ozawa

    HOUSTON JOURNAL OF MATHEMATICS   37 ( 2 ) 627 - 636  2011年  [査読有り]

    　概要を見る

    We consider the incompressible viscoelastic fluid system of the Oldroyd-B model. We prove a regularity criterion del v is an element of L(1)(0, T; L(infinity)) for the 3-D Oldroyd-B system with the initial data (v(0), H(0) - I) is an element of H(2) x W(1,q) with 3 &lt; q &lt;= 6. Global well-posedness of smooth solution is also proven for a regularization model of this Oldroyd-B system in two space dimension.

  • Endpoint Strichartz estimates for the Klein-Gordon equation in two space dimensions and some applications

    Jun Kato, Tohru Ozawa

    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES   95 ( 1 ) 48 - 71  2011年01月  [査読有り]

    　概要を見る

    We prove the endpoint Strichartz estimates for the Klein-Gordon equation in mixed norms on the polar coordinates in two space dimensions. As an application, similar endpoint estimates for the Schrodinger equation in two space dimensions are shown by using the non-relativistic limit. The existence of global solutions for the cubic nonlinear Klein-Gordon equation in two space dimensions for small data is also shown. (C) 2010 Elsevier Masson SAS. All rights reserved.

    DOI

    Scopus

    10
    被引用数
    (Scopus)

  • Global Cauchy Problem for the 2-D Magnetohydrodynamic-alpha Models with Partial Viscous Terms

    Jishan Fan, Tohru Ozawa

    JOURNAL OF MATHEMATICAL FLUID MECHANICS   12 ( 2 ) 306 - 319  2010年05月  [査読有り]

    　概要を見る

    The global Cauchy problem for the 2-D magnetohydrodynamic-alpha models with partial viscous terms is studied. The vanishing limit on alpha is also considered in this paper.

    DOI

    Scopus

    25
    被引用数
    (Scopus)

  • Analytic smoothing effect for global solutions to nonlinear Schrodinger equations

    T. Ozawa, K. Yamauchi

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   364 ( 2 ) 492 - 497  2010年04月  [査読有り]

    　概要を見る

    We prove the global existence of analytic solutions to the Cauchy problem for the cubic Schrodinger equation in space dimension n &gt;= 3 for sufficiently small data with exponential decay at infinity. Minimal regularity assumption regarding scaling invariance is imposed on the Cauchy data. (C) 2009 Elsevier Inc. All rights reserved.

    DOI

    Scopus

    18
    被引用数
    (Scopus)

  • Global Cauchy problems of certain magnetohydrodynamic-&#945; models

    J. Fan, T. Ozawa

    Advances Appl. Math. Sci.   6   169 - 190  2010年  [査読有り]

  • On regularity criterion for the 2D wave maps and the 4D biharmonic wave maps

    J. Fan, T. Ozawa

    GAKUTO International Series, Math. Sci. Appl.   32   69 - 83  2010年  [査読有り]

  • Logarithmically improved regularity criteria for Navier-Stokes and related equations

    Jishan Fan, Tohru Ozawa

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES   32 ( 17 ) 2309 - 2318  2009年11月  [査読有り]

    　概要を見る

    We use an interpolation inequality on Besov spaces to show some logarithmically improved regularity criteria for Navier-Stokes equations, the harmonic heat flow, the Landau-Lifshitz equations, and the Landau-Lifshitz-Maxwell system. Copyright (C) 2009 John Wiley & Sons, Ltd.

    DOI

    Scopus

    14
    被引用数
    (Scopus)

  • REGULARITY CRITERIA FOR A SIMPLIFIED ERICKSEN-LESLIE SYSTEM MODELING THE FLOW OF LIQUID CRYSTALS

    Jishan Fan, Tohru Ozawa

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   25 ( 3 ) 859 - 867  2009年11月  [査読有り]

    　概要を見る

    We consider the hydrodynamic theory of liquid crystals. We prove some regularity criteria for a simplified Ericksen-Leslie system. The existence and uniqueness of global smooth solutions is also proved for a regularization model of this simplified system.

    DOI

    Scopus

    15
    被引用数
    (Scopus)

  • Regularity criterion for a Bona-Colin-Lannes system

    Jishan Fan, Tohru Ozawa

    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS   71 ( 7-8 ) 2634 - 2639  2009年10月  [査読有り]

    　概要を見る

    We prove a regularity criterion of the strong solutions for a Bona-Colin-Lannes system in Besov space. As a byproduct, we show the existence of globally smooth solutions for a symmetric Bona-Colin-Lannes system. (c) 2009 Elsevier Ltd. All rights reserved.

    DOI