Updated on 2022/10/01

写真a

 
WATANABE, Keiichi
 
Affiliation
Faculty of Science and Engineering, Global Center for Science and Engineering
Job title
Assistant Professor(without tenure)
Homepage URL
https://sites.google.com/site/wasedakwatanabe/
Profile

My research mainly focuses on nonlinear partial differential equations describing the motion of viscous fluids. I am interested in the application of some abstract functional analysis and harmonic analysis.

I received the Ph. D. degree in science from Waseda University in 2020 under the supervision of Prof. Yoshihiro Shibata.  I am currently an Assistant Professor in the Global center for Science and Engineering at Waseda University.

Concurrent Post

  • Faculty of Political Science and Economics   School of Political Science and Economics

Education

  • 2017.09
    -
    2020.03

    Waseda University   Graduate School of Fundamental Science and Engineering   Department of Pure and Applied Mathematics  

    Doctoral course

  • 2016.04
    -
    2017.09

    Waseda University   Graduate School of Fundamental Science and Engineering   Department of Pure and Applied Mathematics  

    Master course

  • 2013.04
    -
    2016.03

    Waseda University   School of Fundamental Science and Engineering   Department of Mathematics  

  • 2012.04
    -
    2013.03

    Waseda University   School of Fundamental Science and Engineering  

Degree

  • 2020.03   Waseda University   Ph. D.

Research Experience

  • 2020.04
    -
    Now

    Waseda University   Global Center for Science and Engineering   Assistant Professor

  • 2019.04
    -
    2020.03

    Japan Society for the Promotion of Science   Research Fellowship for Young Scientists (DC2)

Professional Memberships

  • 2017.10
    -
    Now

    The Mathematical Society of Japan

 

Research Areas

  • Mathematical analysis   Partial differential equations

Research Interests

  • Navier-Stokes equations

  • Partial differential equations

Papers

  • Global large solutions and incompressible limit for the compressible Navier–Stokes system with capillarity

    Keiichi Watanabe

    Journal of Mathematical Analysis and Applications   518 ( 1 ) 126675 - 126675  2023.02  [Refereed]

    Authorship：Lead author, Last author, Corresponding author

    DOI

  • Strong time-periodic solutions to chemotaxis–Navier–Stokes equations on bounded domains

    Keiichi Watanabe

    Discrete and Continuous Dynamical Systems   42 ( 11 ) 5577 - 5577  2022.11  [Refereed]

    Authorship：Lead author, Corresponding author

    　View Summary

    <p lang="fr">&lt;p style='text-indent:20px;'&gt;Consider the chemotaxis–Navier–Stokes equations on a bounded convex domain &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ \Omega \subset \mathbb{R}^3 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, where the boundary &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$ \partial \Omega $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; of &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$ \Omega $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; is not necessarily smooth. It is shown that this system admits a unique strong &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$ 2 \pi $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-periodic solution provided that given &lt;inline-formula&gt;&lt;tex-math id="M5"&gt;\begin{document}$ 2 \pi $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-periodic forcing functions are sufficiently small in their natural norm. The result may extend to general cases &lt;inline-formula&gt;&lt;tex-math id="M6"&gt;\begin{document}$ \Omega \subset \mathbb{R}^d $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, &lt;inline-formula&gt;&lt;tex-math id="M7"&gt;\begin{document}$ d \ge 2 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;, if one additionally assumes that &lt;inline-formula&gt;&lt;tex-math id="M8"&gt;\begin{document}$ \partial \Omega $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; is of class &lt;inline-formula&gt;&lt;tex-math id="M9"&gt;\begin{document}$ C^3 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;. The nonnegativity of solutions is also discussed.&lt;/p&gt;</p>

    DOI

  • Local well-posedness of incompressible viscous fluids in bounded cylinders with 90°-contact angle

    Keiichi Watanabe

    Nonlinear Analysis: Real World Applications   65   103489 - 103489  2022.06  [Refereed]

    Authorship：Lead author, Corresponding author

    DOI

  • Stabilization of the chemotaxis–Navier–Stokes equations: Maximal regularity approach

    Keiichi Watanabe

    Journal of Mathematical Analysis and Applications   504 ( 2 ) 125422 - 125422  2021.12  [Refereed]

    Authorship：Lead author, Corresponding author

    DOI

  • Global Solvability of Compressible–Incompressible Two-Phase Flows with Phase Transitions in Bounded Domains

    Keiichi Watanabe

    Mathematics   9 ( 3 ) 258 - 258  2021.01  [Refereed]  [Invited]

    Authorship：Lead author, Corresponding author

    DOI

  • Strong solutions to compressible–incompressible two-phase flows with phase transitions

    Keiichi Watanabe

    Nonlinear Analysis: Real World Applications   54   103101 - 103101  2020.08  [Refereed]

    Authorship：Lead author, Corresponding author

    DOI

  • The Navier–Stokes equations in exterior Lipschitz domains: L -theory

    Patrick Tolksdorf, Keiichi Watanabe

    Journal of Differential Equations    2020.04  [Refereed]

    DOI

  • Compressible–Incompressible Two-Phase Flows with Phase Transition: Model Problem

    Keiichi Watanabe

    Journal of Mathematical Fluid Mechanics   20 ( 3 ) 969 - 1011  2018.09  [Refereed]

    Authorship：Lead author, Corresponding author

    DOI

▼display all

Misc

  • Stability of rotating liquid

    Keiichi Watanabe

        265 - 272  2021

    Authorship：Lead author, Corresponding author

    Research paper, summary (national, other academic conference)  

  • The Stokes operator in exterior Lipschitz domains

    Keiichi Watanabe

    RIMS Kôkyûroku   2168   44 - 56  2020.08  [Invited]

    Authorship：Lead author, Corresponding author

    Article, review, commentary, editorial, etc. (international conference proceedings)  

  • On the local solvability of compressible-incompressible two-phase flows with phase transitions in general domains

    Keiichi Watanabe

    第40回発展方程式若手セミナー報告集     237 - 244  2018

    Authorship：Lead author, Corresponding author

    Research paper, summary (national, other academic conference)  

Research Projects

  • 接触角を生成する流体方程式の適切性

    日本学術振興会  科学研究費助成事業 若手研究

    Project Year :

    2021.04
    -
    2026.03
     

    渡邊 圭市

  • Mathematical analysis of the Navier-Stokes equations in exterior domains

    Waseda University  Special Research Projects

    Project Year :

    2022.06
    -
    2023.03
     

    Keiichi Watanabe

  • DAAD-Waseda University Partnership Programme

    Der Deutsche Akademische Austauschdienst 

    Project Year :

    2021.04
    -
    2023.03
     

    Keiichi Watanabe, Jürgen Saal

  • Navier-Stokes equations in non-smooth domains

    Waseda University  Waseda University Grant for Special Research Projects

    Project Year :

    2021.06
    -
    2022.03
     

    Keiichi Watanabe

  • 接触角を生成する非圧縮性粘性流体の数学解析

    日本学術振興会  科学研究費助成事業 研究活動スタート支援

    Project Year :

    2020.09
    -
    2022.03
     

    渡邊圭市

  • Mathematical analysis of the Navier-Stokes equations with moving contact angles

    Waseda University  Special Research Projects

    Project Year :

    2020.06
    -
    2021.03
     

    Keiichi Watanabe

  • Free boundary problem of compressible-incompressible viscous two-phase flows with phase transitions in unbounded domains

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for JSPS Fellows

    Project Year :

    2019.04
    -
    2020.03
     

    Keiichi Watanabe

  • Mathematical analysis of compressible-incompressible two-phase flows with surface tension and phase transition

    Waseda Research Institute for Science and Engineering  Early-Bird Program Fellowships

    Project Year :

    2018.05
    -
    2019.03
     

    Keiichi Watanabe

▼display all

Presentations

▼display all

Specific Research

  • 境界が滑らかでない領域におけるナビエ・ストークス方程式の数学解析

    2021  

    　View Summary

    本年度は外部領域リプシッツ領域におけるストークス半群の減衰評価を研究した．ここで，外部リプシッツ領域とは，全空間における有界リプシッツ領域の補集合を指す．本研究では，岩下（1989）の局所エネルギー減衰評価を外部リプシッツ領域の場合に拡張し，全空間におけるストークス方程式の解と有界リプシッツ領域におけるかいを適当な切り落とし関数により繋ぎ合わせることでパラメトリクスを構成し，ストークス半群の勾配のLp-Lq評価を証明した．特に，この減衰率は，境界がなめらかな場合と同様であることがわかり，Maremonti-Solonnikov（1997）の結果から本研究の結果は最適であることがわかった．

  • 接触角を生成するナビエ・ストークス方程式の数学解析

    2020  

    　View Summary

    接触角を生成するナビエ・ストークス方程式の自由境界問題の時間局所適切性を示した．この問題は接触角付近に特異性が生じることが知られており，この特異性を除去するためにこれまで様々な数理モデルが提唱されてきた．本研究では，Wilke (2020) と同様に，柱状領域において流体が部分的に占められている状況において，接触角が90°に固定されている場合を考察し，強解を最大Lp-Lq正則性のクラスで得た．また，関連する研究として，ナビエ・ストークス方程式の自由境界問題の定常解の安定性に関する結果も得た．これらの結果は単著論文としてまとめ，現在査読付き国際学術誌に投稿中である．

 

Syllabus

▼display all

Teaching Experience

  • Calculus B (2)

    Waseda University  

  • Survey of Modern Mathematical Sciences A

    Waseda University  

  • Ordinary Differential Equations (2)

    Waseda University  

  • Foundations of Analysis 1

    Waseda University  

  • Advanced Analysis

    Waseda University  

  • Survey of Modern Mathematical Sciences B

    Waseda University  

  • Calculus C (1)

    Waseda University  

  • Ordinary Differential Equations (1)

    Waseda University  

  • Exercise for Fundamental Mathematics

    Waseda University  

  • Measure Theory

    Waseda University  

▼display all

 

Academic Activities

▼display all