Updated on 2024/02/22

写真a

 
HISHIDA, Toshiaki
 
Organization
Graduate School of Mathematics Division of Mathematics Natural Mathematics Professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science
Title
Professor

Degree 1

  1. 博士(理学) ( 1993.6   早稲田大学 ) 

Research Interests 1

  1. Navier-Stokes equation

Research Areas 1

  1. Others / Others  / 数学/函数方程式論

Professional Memberships 1

  1. Mathematical Society of Japan

Awards 1

  1. Analysis Prize

    2007.9   Mathematical Society of Japan  

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    Country:Japan

 

Papers 31

  1. Stability of time-dependent motions for fluid-rigid ball interaction Reviewed

    Toshiaki Hishida

    J. Math. Fluid Mech.   Vol. 26 ( Paper No. 17 )   2024.2

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00021-024-00854-7

  2. Spatial Pointwise Behavior of Time-Periodic Navier-Stokes Flow Induced by Oscillation of a Moving Obstacle

    Hishida Toshiaki

    JOURNAL OF MATHEMATICAL FLUID MECHANICS   Vol. 24 ( 4 )   2022.11

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  3. On the asymptotic structure of steady Stokes and Navier-Stokes flows around a rotating two-dimensional body Reviewed International coauthorship International journal

    Toshiaki Hishida, Mads Kyed

    Pacific Journal of Mathematics   Vol. 315 ( 1 ) page: 89 - 109   2021.11

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2140/pjm.2021.315.89

    Web of Science

  4. Attainability of time-periodic flow of a viscous liquid past an oscillating body Invited Reviewed International coauthorship International journal

    Giovanni P. Galdi, Toshiaki Hishida

    Journal of Evolution Equations   Vol. 21 ( 3 ) page: 2877 - 2890   2021.9

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00028-020-00661-3

    Web of Science

  5. An alternative proof of Lq-Lr estimates of the Oseen semigroup in higher dimensional exterior domains Invited Reviewed

    Toshiaki Hishida

    SN Partial Differential Equations and Applications   Vol. 2 ( paper No.32 )   2021

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    Authorship:Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: https://doi.org/10.1007/s42985-021-00086-8

  6. Optimal boundary control for steady motions of a self-propelled body in a Navier-Stokes liquid Reviewed International coauthorship International journal

    Hishida Toshiaki, Silvestre Ana Leonor, Takahashi Takeo

    ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS   Vol. 26   2020.11

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1051/cocv/2020073

    Web of Science

  7. Decay Estimates of Gradient of a Generalized Oseen Evolution Operator Arising from Time-Dependent Rigid Motions in Exterior Domains Reviewed International journal

    Hishida Toshiaki

    ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS   Vol. 238 ( 1 ) page: 215 - 254   2020.10

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00205-020-01541-3

    Web of Science

  8. Large time behavior of a generalized Oseen evolution operator, with applications to the Navier-Stokes flow past a rotating obstacle Reviewed

    Hishida Toshiaki

    MATHEMATISCHE ANNALEN   Vol. 372 ( 3-4 ) page: 915-949   2018.12

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00208-018-1649-0

    Web of Science

  9. Navier-Stokes Flow Past a Rigid Body: Attainability of Steady Solutions as Limits of Unsteady Weak Solutions, Starting and Landing Cases

    Hishida Toshiaki, Maremonti Paolo

    JOURNAL OF MATHEMATICAL FLUID MECHANICS   Vol. 20 ( 2 ) page: 771-800   2018.6

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/s00021-017-0344-3

    Web of Science

  10. Stationary Navier-Stokes flow in exterior domains and Landau solutions Invited Reviewed

    Toshiaki Hishida

    Handbook of Mathematical Analysis in Mechanics of Viscous Fluids     page: 299 - 339   2018

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    Authorship:Corresponding author   Language:English  

  11. A boundary control problem for the steady self-propelled motion of a rigid body in a Navier-Stokes fluid

    Hishida Toshiaki, Silvestre Ana Leonor, Takahashi Takeo

    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE   Vol. 34 ( 6 ) page: 1507-1541   2017

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.anihpc.2016.11.003

    Web of Science

  12. Stability of time-dependent Navier-Stokes flow and algebraic energy decay Reviewed

    Toshiaki Hishida and Maria Schonbek

    Indiana Univ. Math. J.   Vol. 65 ( 4 ) page: 1307-1346   2016.8

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 1307-1346

  13. L^q-L^r estimate of the Oseen flow in plane exterior domains Reviewed

    Toshiaki Hishida

    J. Math. Soc. Japan   Vol. 68 ( 1 ) page: 295-346   2016.1

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.2969/jmsj/06810295

  14. Asymptotic structure of steady Stokes flow around a rotating obstacle in two dimensions Invited Reviewed

    Toshiaki Hishida

    Springer Proc. Math. Statistics   Vol. 183   page: 95-137   2016

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1007/978-4-431-56457-7

    arXiv

  15. On the asymptotic stability for small initial disturbance of Navier-Stokes flow in a two-dimensional aperture domain Invited Reviewed

    Toshiaki Hishida and Takayuki Kubo

    Gakuto International Series Mathematical Sciences and Applications   Vol. 37   page: 183-192   2015.4

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  16. Decay estimates of the Oseen flow in two-dimensional exterior domains Invited Reviewed

    Toshiaki Hishida

    Gakuto International Series Mathematical Sciences and Applications   Vol. 37   page: 63-87   2015.4

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  17. Mathematical analysis of the equations for incompressible viscous fluid around a rotating obstacle Invited Reviewed

    Toshiaki Hishida

    Sugaku Expositions   Vol. 26 ( 2 ) page: 149-179   2013.12

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    Language:English  

  18. On the relation between the large time behavior of the Stokes semigroup and the decay of steady Stokes flow at infinity Reviewed

    Toshiaki Hishida

    Progress in Nonlinear Diff. Eq. and Their Appl.   Vol. 60   page: 343-355   2011

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    Language:English   Publishing type:Research paper (scientific journal)  

  19. Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle Reviewed

    Reinhard Farwig, Toshiaki Hishida

    Math. Nachr.   Vol. 284 ( 16 ) page: 2065-2077   2011

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    Language:English   Publishing type:Research paper (scientific journal)  

  20. Asymptotic profile of steady Stokes flow around a rotating obstacle Reviewed

    Reinhard Farwig, Toshiaki Hishida

    Manuscripta Math.   Vol. 136   page: 315-338   2011

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    Language:English   Publishing type:Research paper (scientific journal)  

  21. The Navier-Stokes flow around a rotating obstacle with time-dependent body force Reviewed

    Toshiaki Hishida

    Banach Center Publ.   Vol. 86   page: 149-162   2009

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    Language:English   Publishing type:Research paper (scientific journal)  

  22. *L_p-L_q estimate of the Stokes operator and Navier-Stokes flows in the exterior of a rotating obstacle Reviewed

    Toshiaki Hishida, Yoshihiro Shibata

    Arch. Rational Mech. Anal.   Vol. 193 ( 2 ) page: 339-421   2009

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    Language:English   Publishing type:Research paper (scientific journal)  

  23. Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle Invited Reviewed

    Reinhard Farwig, Toshiaki Hishida

    Ann. Univ. Ferrara Sez. VII. Sci. Mat.   Vol. 55 ( 2 ) page: 263-277   2009

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

  24. Mathematical analysis of the Navier-Stokes flow around a rotating obstacle

    Toshiaki Hishida

    COE Lecture Note (Kyushu University)   Vol. 20   page: 25-41   2009

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    Language:English  

  25. *回転する障害物の周りでの非圧縮粘性流体の方程式の数学解析 Reviewed

    菱田俊明

    数学   Vol. 60 ( 1 ) page: 68-94   2008

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    Language:Japanese  

  26. Decay estimates of the Stokes flow around a rotating obstacle Reviewed

    Toshiaki Hishida and Yoshihiro Shibata

    RIMS Kokyuroku Bessatsu   Vol. 1   page: 167-186   2007

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    Language:English   Publishing type:Research paper (scientific journal)  

  27. *Stationary Navier-Stokes flow around a rotating obstacle Reviewed

    R. Farwig and T. Hishida

    Funkcial. Ekvac.   Vol. 50 ( 3 ) page: 371-403   2007

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    Language:English   Publishing type:Research paper (scientific journal)  

  28. Steady motions of the Navier-Stokes fluid around a rotating body Reviewed

    Toshiaki Hishida

    Adv Studies Pure Math.   Vol. 47-1   page: 117-136   2007

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    Language:English   Publishing type:Research paper (scientific journal)  

  29. L^q estimates of weak solutions to the stationary Stokes equations around a rotating body Reviewed

    Toshiaki Hishida

    J. Math. Soc. Japan   Vol. 58 ( 3 ) page: 743-767   2006

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    Language:English   Publishing type:Research paper (scientific journal)  

  30. *The nonstationary Stokes and Navier-Stokes flows through an aperture Reviewed

    Toshiaki Hishida

    Adv. Math. Fluid Mech.   Vol. 3   page: 79-123   2004

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    Language:English   Publishing type:Research paper (scientific journal)  

  31. L^q-theory of a singular ``winding'' integral operator arising from fluid dynamics Reviewed

    R. Farwig, T. Hishida and D. Mueller

    Pacific J. Math.   Vol. 215 ( 2 ) page: 297-312   2004

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    Language:English   Publishing type:Research paper (scientific journal)  

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Presentations 33

  1. Stability of self-propelled motions of a rigid ball in a viscous incompressble fluid Invited

    Toshiaki Hishida

    2023.12.11  RIMS, Kyoto University

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    Event date: 2023.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Kyoto   Country:Japan  

  2. Stability of time-dependent motions for fluid-rigid ball interaction Invited International conference

    Toshiaki Hishida

    Internal Workshop on Multi-Phase Flows: Analysis, Modelling and Numerics  2022.12.5  Waseda University

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    Event date: 2022.12

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Tokyo   Country:Japan  

  3. Spatial pointwise behavior of time-periodic Navier-Stokes flow induced by oscillation of a moving obstacle Invited International conference

    Toshiaki Hishida

    East Asian Workshop on Partial Differential Equations in Fluid Dynamics  2022.1.27  PDE group in Tokyo Institute of Technology

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    Event date: 2022.1

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Tokyo   Country:Japan  

  4. Optimal boundary control for steady motions of a self-propelled body in a viscous incompressible fluid Invited International coauthorship International conference

    Toshiaki Hishida

    Fluids under Control  2021.8.25  Czech Academy of Sciences

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    Event date: 2021.8

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Prague   Country:Czech Republic  

  5. Optimal boundary control for steady motions of a self-propelled body in a viscous incompressible fluid Invited International coauthorship

    Toshiaki Hishida

    Fudan International Seminar on Analysis, PDEs and Fluid Mechanics  2021.4.22  Fudan University

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    Event date: 2021.4

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Fudan   Country:China  

  6. Asymptotic structure of steady Stokes flow around a rotating obstacle in 2D International conference

    Toshiaki Hishida

    Asymptotic Problems: Elliptic and Parabolic Issues 

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    Event date: 2015.6

    Language:English   Presentation type:Oral presentation (general)  

    Country:Lithuania  

  7. Asymptotic structure of steady viscous incompressible flow around a rotating obstacle in 2D International conference

    Toshiaki Hishida

    International Conference on Mathematical Fluid Dynamics -Present and Future 

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    Event date: 2014.11

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  8. Stability of time-dependent Navier-Stokes flow and algebraic energy decay International conference

    Toshiaki Hishida and Maria Schonbek

    Vorticity, Rotation and Symmetry (III) 

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    Event date: 2014.5

    Language:English   Presentation type:Oral presentation (general)  

    Country:France  

  9. Decay estimates of the Oseen semigroup in two-dimensional exterior domains International conference

    Toshiaki Hishida

    Geophysical Fluid Dynamics 

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    Event date: 2013.2

    Language:English   Presentation type:Oral presentation (general)  

    Country:Germany  

  10. Stability and asymptotic structure of steady Navier-Stokes flows in exterior and aperture domains International conference

    Toshiaki Hishida

    SIAM Conference on Analysis of PDEs 

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    Event date: 2011.11

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:United States  

  11. Resolution of the Stokes paradox by the rotation of bodies in the plane International conference

    Toshiaki Hishida

    International Conference on Fluid and Gas Dynamics 

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    Event date: 2011.9

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:China  

  12. Resolution of the Stokes paradox by the rotation of bodies in the plane

    Toshiaki Hishida

    Mathematical Analysis in Fluid and Gas Dynamics 

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    Event date: 2011.7

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  13. 2D flow around a rotating obstacle International conference

    International Conference on Evolution Equations 

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    Event date: 2010.10

    Language:English   Presentation type:Oral presentation (invited, special)  

  14. 2D flow around a rotating body International conference

    The 8th AIMS Conference on Dynamical Systems, Differential equations and Applications 

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    Event date: 2010.5

    Language:English   Presentation type:Oral presentation (invited, special)  

  15. Leading profile of the steady Navier-Stokes flow around a rotating body International conference

    Mathematical Fluid Dynamics Launching Workshop 

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    Event date: 2009.4

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  16. Mathematical analysis of the Navier-Stokes flow around a rotating obstacle

    Math-for-Industry Tutorial: Spectral theories of non-Hermitian operators and their application 

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    Event date: 2009.3

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  17. Asymptotic profile of the steady Stokes flow around a rotating obstacle International conference

    International workshop on Mathematical Fluid Dynamics 

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    Event date: 2008.9

    Language:English   Presentation type:Oral presentation (invited, special)  

  18. Asymptotic profile of the steady and unsteady Stokes flows around a rotating obstacle International conference

    Conference on Parabolic and Navier-Stokes Equations 

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    Event date: 2008.9

    Language:English   Presentation type:Oral presentation (invited, special)  

  19. Asymptotic profile of the steady Stokes flow around a rotating obstacle

    New Aspects and Development of Mathematical Analysis in Nonlinear Phenomena 

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    Event date: 2008.5

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  20. Asymptotic profile of the steady Stokes flow around a rotating obstacle International conference

    International Conference on Vorticity, rotation and symmetry 

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    Event date: 2008.5

    Language:English   Presentation type:Oral presentation (invited, special)  

  21. 回転する障害物の周りでの非圧縮粘性流体の方程式の数学解析

    日本数学会春季年会函数方程式論分科会・特別講演 

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    Event date: 2008.3

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  22. Asymptotic profile of the steady flow around a rotating obstacle International conference

    Workshop on Fluid-Structure Interactions and Related Topics 

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    Event date: 2007.10

    Language:English   Presentation type:Oral presentation (invited, special)  

  23. The Navier-Stokes flow around a rotating obstacle with time-dependent body force International conference

    International Conference of Theoretical and Numerical Fluid Mechanics III 

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    Event date: 2007.8

    Language:English   Presentation type:Oral presentation (invited, special)  

  24. Periodic solutions of the Navier-Stokes equations around a rotating obstacle International conference

    Conference on Nonlocal and Abstract Parabolic Equations and Their Applications 

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    Event date: 2007.6

    Language:English   Presentation type:Oral presentation (invited, special)  

  25. Stability of the Navier-Stokes flow around a rotating obstacle International conference

    Conference on Parabolic and Navier-Stokes Equations 

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    Event date: 2006.9

    Language:English   Presentation type:Oral presentation (invited, special)  

  26. On existence and stability of exterior stationary Navier-Stokes flows around a rotating obstacle International conference

    Evolution Equations 2006 in memory of Guenter Lumer 

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    Event date: 2006.8

    Language:English   Presentation type:Oral presentation (invited, special)  

  27. Stability of the Navier-Stokes flow around a rotating obstacle International conference

    Darmstaedter Analysis Tag zum Thema Navier-Stokes 

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    Event date: 2006.5

    Language:English   Presentation type:Oral presentation (invited, special)  

  28. Stability of the Navier-Stokes flow around a rotating obstacle

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    Event date: 2006.2

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  29. Decay estimates of the Stokes flow around a rotating obstacle

    Kyoto Conference on the Navier-Stokes equations and their applications 

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    Event date: 2006.1

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  30. Stationary Navier-Stokes flows around a rotating obstacle International conference

    The 11th EQUADIFF: International Conference on Differential Equations 

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    Event date: 2005.7

    Language:English   Presentation type:Oral presentation (invited, special)  

  31. Steady motions of the Navier-Stokes fluid around a rotating body

    MSJ-IRI 2005 "Asymptotic Analysis and Singularity" 

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    Event date: 2005.7

    Language:English   Presentation type:Oral presentation (general)  

    Country:Japan  

  32. L^q estimates for the Stokes equations around a rotating body

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    Event date: 2004.7

    Language:English   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

  33. Aperture domain における Navier-Stokes 方程式

    日本数学会春季年会・函数方程式論分科会・特別講演 

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    Event date: 2003.3

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Country:Japan  

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KAKENHI (Grants-in-Aid for Scientific Research) 8

  1. 非圧縮粘性流と相互作用する物体の運動の数学解析

    Grant number:22K03372  2022.4 - 2025.3

    科学研究費助成事業  基盤研究(C)

    菱田 俊明

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    Authorship:Principal investigator 

    Grant amount:\4290000 ( Direct Cost: \3300000 、 Indirect Cost:\990000 )

    3次元空間において無限遠まで拡がる非圧縮粘性流体の中を物体が運動している。物体は剛体とし、したがってその運動は並進と回転で記述される。物体と流体、双方の運動の相互作用の問題においては、流体の占める外部領域が運動する物体の補集合としてこれも未知であるから、自由度6の自由境界問題と見られるが、実際に解析するときは運動する物体に固定した座標系によって方程式を書き直す。本研究の核心をなす最も基本的な問題は、その座標系によって定常あるいは時間周期的な運動を主流として、その漸近安定性と擾乱の時間減衰率、および主流じたいの空間無限遠での減衰構造、さらに物体の運動の境界上での最適制御である。

  2. 粘性流体の中の物体の運動の制御と安定性の数学解析

    Grant number:18K03363  2018.4 - 2023.3

    科学研究費助成事業  基盤研究(C)

    菱田 俊明

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\4420000 ( Direct Cost: \3400000 、 Indirect Cost:\1020000 )

    3次元空間または2次元平面の中に運動する剛体があるとして、空間次元および運動の状態に応じた解(定常解、時間周期解)の空間無限遠での減衰構造、またその解の安定性やattainabilityを擾乱の長時間挙動と共に明らかすることは本研究の主題のひとつである。この主題について、本年度に研究代表者が公表した成果は以下のとおりである。時空漸近挙動が論点であるとき、2次元流のほうが3次元流よりも格段に難しい理由が幾つかあり、特に定常流に対するStokesのパラドックスはまず挙げなくてはならない困難である。障害物の回転の効果によってStokesのパラドックスが解消されることは研究代表者の2016年発表の論文の成果であったが、異なる視点からそれを再度証明すると共に、線型化方程式の解の新しい評価を求めた。さらに、その評価を効果的に用いて、スケ一ル臨界な減衰度をもつNavier-Stokes流の空間無限遠での漸近展開を導出し、特にそのleading項の形を明らかにした。次に、2次元を除くいかなる空間次元であっても、障害物の並進運動の周りでの線型化によって得られるOseen半群の時間減衰評価について、従来の証明よりも平易な別証明を与えた。この証明方法の特徴はresolventを使わないことであり、従って線型化方程式が非自励系であっても解析を進められる。実際、主流が時間依存である場合への応用として、障害物の時間周期的な並進運動から決まる時間周期解のattainabilityを示した。ところで、障害物の振動の仕方は様々であるが、時間周期解の一意存在を許すための条件は先行研究において限定的なものであった。本研究では研究代表者自身による発展作用素の減衰評価を援用して、並進の方向と回転軸の方向が全く一般な状況のもとで3次元時間周期解の存在と一意性を証明し、その空間無限遠での漸近挙動を詳しく調べた。
    非圧縮粘性流体の中の物体の運動の制御と安定性の数学的解明、また関連する諸問題の数学的基礎を与えることを研究目的としている。制御や安定性と関わる問題として、定常解および時間周期解の空間無限遠での減衰構造、それらの主流まわりでの線型化作用素の解析は代表的なものである。主流が定常解のときはスペクトル解析が中心となる一方で、主流が時間周期解をはじめとする時間依存な流れの場合には、スペクトル解析の代替として研究代表者が2020年発表の論文で提示した新しい方法があり、そのアイデアは本年度の研究でも大いに活用されている。実際、そのような解析の応用によって、先行研究をすべて包括する最も一般な剛体の振動に対して時間周期解を一意的に構成した。この解は小さい擾乱に対して安定であると共に、適当な条件のもとで空間無限遠での各点減衰評価を持つものである(専門誌で査読中、またarXiv:2203.14778で公開中)。特にwake regionを有するための十分条件を提示できたことは意義深い。また、得られた時間周期解に対するFinnのstarting問題について、これが肯定的に解決される場合にその周期解はattainableであるといい、安定性の証明よりもさらに繊細な議論を要するが、剛体がスピンはせずに振動し、時間周期的な並進運動の一周期での平均がゼロであるときに時間周期解のattainabilityを示すことができた。より一般な剛体の振動から決まる周期解のattainabilityは今後の課題としたい。2次元平面流については、時間周期解の特別な場合とみなせる定常解の深い研究をまず要するが、Stokesのパラドックスを解消する何らかの機構を手がかりとするほかなく、回転運動がそのような機構となりうることを非線型問題の解の空間無限遠での漸近展開を通して示したことは今後の研究の展開に示唆を与えるものである。
    今後の研究課題として最も重要なものは、流体と剛体の相互作用の解析である。研究代表者が2020年発表の論文において定常的なself-propelled運動の境界上での最適制御問題を考察したが、そこで得られた解の安定性およびattainabilityは未解決である。そもそも、一般な形状の剛体運動の周りでの時間大域解の一意存在に関する先行研究は、有限時間爆発を防ぐような解のアプリオリ評価によるもので、解の長時間挙動には何も答えていない。これまでのところ、時間大域解の漸近挙動についてのただひとつの成果は剛体が球体の場合であって、しかも主流は自明解に限られる。Tucsnak氏らによって近年得られたその成果はmonolithic approachに従い流体と剛体両者の運動方程式を一体でとらえたうえで線型化方程式の解(fluid-structure半群)の減衰評価に基づくもので、線型のレベルでは球体に限る必要はないが、非線型方程式を解く際に回転運動がもたらす重要な非線型項があると立ち行かない。研究代表者が開発した非自励系に対する解析方法はこの困難に正面から取り組んで克服する方法を示唆しており、成功すればfluid-structure相互作用の安定性理論の構築につながるものである。また、研究代表者のその方法は空間3次元では機能するが、2次元平面流に対してはそのままの形では働かない。そこで、fluid-structureへ進む以前にいったん流体の運動方程式を切り離して非自励な線型化方程式が生成する発展作用素の長時間挙動を考察する。典型的な場合は時間周期解周りでの線型化であるが、定常解周りに限っても安定性が示されているのは定常的な並進運動の場合についての近年の研究だけであり、剛体が回転する場合の解析を本研究で得られた定常解の空間無限遠での漸近展開の主要項に注目して進めたい。

  3. 粘性流体の中の物体の運動の制御と安定性の数学解析

    2018.4 - 2021.3

    科学研究費補助金  基盤研究(C)

    菱田俊明

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    Authorship:Principal investigator 

  4. Mathematical analysis of fluid-structure interaction

    Grant number:15K04954  2015.4 - 2019.3

    Hishida Toshiaki

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    Authorship:Principal investigator 

    Grant amount:\4680000 ( Direct Cost: \3600000 、 Indirect Cost:\1080000 )

    I analyzed a problem arising from fluid-structure interaction and some related issues, where the fluid is incompressible as well as viscous, while the structure is assumed to be a rigid body. In 3D case the boundary controllability of a self-propelled motion of a body, whose motion is prescribed but not too large, was proved. Toward analysis of this solution, I deduced a large time behavior of the evolution operator generated by a linearized system around time-dependent rigid motions. A new result on the starting problem in 3D proposed by Finn was also provided. In 2D case an asymptotic representation of steady flows at spatial infinity around a rotating body was discovered. I also deduced a temporal decay estimate of the Oseen semigroup past a translating body in 2D.

  5. 非圧縮粘性流と物体の運動の相互作用の数学解析

    2015.4 - 2018.3

    科学研究費補助金  基盤研究(C)

    菱田俊明

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    Authorship:Principal investigator 

  6. Mathematical analysis on decay structure of viscous incompressible flow affected by motions of obstacle

    2012.4 - 2015.3

    Grant-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research(C)

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    Authorship:Principal investigator 

  7. 粘性流体の中の物体の運動の数学解析

    2007.4 - 2011.3

    科学研究費補助金  基盤研究(C)

    菱田 俊明

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    Authorship:Principal investigator 

  8. Mathematical Analysis of stability of viscous incompressible flows in several unbounded domains

    2004.4 - 2007.3

    Grant-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research(C)

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    Authorship:Principal investigator 

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Teaching Experience (On-campus) 13

  1. 解析学概論

    2015

  2. 解析学要論(常微分方程式論)

    2015

  3. 解析学要論

    2014

  4. 複素関数論

    2014

  5. 偏微分方程式特論

    2013

  6. 解析学要論

    2013

  7. 複素関数論

    2013

  8. 解析学概論

    2012

  9. 解析学要論

    2012

  10. Complex Analysis

    2011

  11. 解析学概論

    2011

  12. 解析学要論

    2011

  13. 解析学続論

    2009

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Teaching Experience (Off-campus) 2

  1. 解析学

    2018.4 - 2019.3 Osaka City University)

  2. 解析学

    2014.4 - 2015.3 Tohoku University)