Updated on 2021/05/31

写真a

 
HISHIDA, Toshiaki
 
Organization
Graduate School 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 26

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

    Galdi Giovanni P., Hishida Toshiaki

    JOURNAL OF EVOLUTION EQUATIONS     2021.1

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

    DOI: 10.1007/s00028-020-00661-3

    Web of Science

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

    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

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

    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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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)  

  11. 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)  

  12. 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  

  13. 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)  

  14. 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)  

  15. 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)  

  16. 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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  17. 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  

  18. 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)  

  19. *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)  

  20. *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  

  21. 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)  

  22. *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)  

  23. 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)  

  24. 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)  

  25. 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)  

  26. *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)  

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Presentations 28

  1. 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  

  2. 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  

  3. 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  

  4. 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  

  5. 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  

  6. 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  

  7. 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  

  8. 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)  

  9. 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)  

  10. 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  

  11. 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  

  12. 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)  

  13. 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)  

  14. 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  

  15. 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)  

  16. 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  

  17. 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)  

  18. 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)  

  19. 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)  

  20. 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)  

  21. 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)  

  22. 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)  

  23. 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  

  24. 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  

  25. 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)  

  26. 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  

  27. 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  

  28. 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) 7

  1. 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 

  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 - 2021.3

    菱田 俊明

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    Authorship:Principal investigator 

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

    3次元空間内でのself-propelled条件を満たす物体の運動とその周りでの流体の運動の相互作用を考察した。ただし、物体に固定した座標系で見て時間定常的な運動を考える。定常的なself-propelled条件は、物体が流体におよぼす力とトルクがいずれも消えていることを表している。剛体の並進速度と回転角速度を小さく与えるときに、それを達成する境界上での制御関数の存在はすでに研究代表者の研究により知られていたが、本研究では2通りの属性をみたす(境界上で指定された小さなportion上に台をもつ、あるいは境界上の各点で接している)制御関数の内で、物体にかかる抵抗を最小化する最適制御の存在を示し、さらにその最適制御が満たす必要条件を求めた(専門誌で査読中、またarXiv:2003.03991で公開中)。また、2次元平面上で一様に回転する剛体の外部でスケ一ル臨界減衰する定常Navier-Stokes流の無限遠での漸近展開の主要項を決定した(専門誌で査読中、またarXiv:1809.03164で公開中)。再び空間3次元の問題へ戻り、上記の最適制御解の安定性を考察するとき、剛体の運動が時間によって変動するときの非自励な線型化方程式の初期値問題の解の長時間挙動が重要な鍵となる。その解を実現する発展作用素の0階の減衰評価は研究代表者の研究により知られていたが、本研究では空間1階gradientの減衰評価を証明した(Arch. Rational Mech. Anal.掲載決定)。その成果はStokes半群やOseen半群を含む自励系に対する結果をすべて包括している。その応用の一つとして、流体中をスピンはせずに振動する剛体周りでの定常解のattainabilityを証明した(専門誌で査読中、またarXiv:2001.07292で公開中)。
    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する。空間3次元の剛体のself-propelled運動の境界上での制御の問題について、少なくとも2種類の制御方法が知られていたが、制御方法(制御関数の属性)をひとつ定めるとき、物体にかかる抵抗最小化の意味での最適制御の存在や特徴付けは解かれずに残っていた。それが得られたことは成果であった。特に最適制御の必要条件の導出方法は、よく知られたLagrangeの方法のここでの議論の枠組みにフィットする形での洗練であり、そのやりかた自体も同種の最適制御問題への展望を与えるものである。また、その最適制御解の安定性やattainabilityを論じるうえで、剛体の並進速度と回転角速度が時間に依存する場合の線型化方程式の初期値問題の解析が欠かせない。特にその時間減衰評価を外部領域で求めることは自励系であっても難しい問題であるが、ここで考察するのは非自励系であり、通常のスペクトル解析は働かない。この系のエネルギ一関係式を活用した0階の減衰評価は研究代表者の以前の成果であるが、その0階に対する知見を活かした1階微分の減衰評価は、結果および証明方法のいずれも新しく、Stokes半群とOseen半群、および回転も伴うときのそれらの半群の評価をすべて再現するとともに、幅広い応用がある。典型的な応用はstarting問題への応用である。starting問題とは、初期時刻で静止している物体が運動し始めて、有限時間後に一様な運動に至るときのその周りでの流れの長時間挙動を問うものであるが、最終的な物体の運動が一様並進という最もシンプルな場合を除いて、上記の発展作用素による解析が本質的に必要である。スピンなしの振動や一様回転は、その重要な例である。
    今後の研究で最も重要な主題は、ここまで述べてきた物体と流体の運動の相互作用の初期値問題の解の長時間挙動を求めることである。ただし、空間次元は3次元とする。小さい初期値に対して、時間大域解の存在が自乗可積分空間の枠組みで知られているが、それ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。この主題について、最近フランスのTucsnakのグル一プによる重要な進展があった。彼らの着眼は、流体の運動方程式と剛体の運動方程式を同時に捉えるfluid-structure半群の減衰評価の導出とその応用であり、部分的な成果を得た。ここで部分的と述べたのは、物体を球体に限定したためである。彼らのアイデアは興味深いが、弱点は座標変換後に回転運動がもたらす重要な項を上記のfluid-structure半群からの摂動として扱えないことであり、球体であればその項が現われないのである。ここまで述べてきた本研究の成果は、まさにこの困難を正面から取り扱ったものであり、物体の形状が何であっても、与えられた並進速度と回転角速度が時間変数に関して有界かつヘルダ一連続である限り、上記の項を伴う線型化作用素の生成する発展作用素の減衰度を決定した。その結果それ自体でなくともその論証における考え方は、上記のTucsnakらによる最新の成果がのりこえられなかった困難をどうやって克服すればよいのか、その方法を示唆している。これの実行、すなわちfluid-structure発展作用素の減衰評価の導出とその応用がまずやるべきことである。その先に本研究によって得られた最適制御解の安定性の問題があるが、物体のself-propelled運動によって、流れの空間無限遠での減衰が良いので、上記の発展作用素が支配的であると期待できる。

  3. 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.

  4. 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 

  5. 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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  6. 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 

  7. 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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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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