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Clarification of the mathematical structure of fluid-dynamical and electromagnetic phenomena depending on topological properties of the domain.

Research Project

Project/Area Number 21540179
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNara Women's University

Principal Investigator

YANAGISAWA Taku  奈良女子大学, 理学部, 教授 (30192389)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords関数方程式 / 境界値問題 / Hodge分解 / ナビエ・ストークス方程式 / 磁気流体力学方程式 / Navier-Stokes方程式 / 分解定理 / Div-Curl lemma / 流体力学
Research Abstract

Several phenomena of fluid or electromagnetism seem to have close relation to topological properties of the domain in which the phenomena occur. Here the topological properties of the domain mean, for example, the number of the inner boundary components and the genus of the outer boundary component of the domain. This research discusses new analytical methods based on the decomposition theorem of vector fields on the domain and the singular perturbation, aiming at clarifying the mathematical structure of such fluid-dynamical and electromagnetic phenomena depending on topological properties of the domain.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (52 results)

All 2012 2011 2010 2009

All Journal Article (18 results) (of which Peer Reviewed: 15 results) Presentation (34 results)

  • [Journal Article] Leray's inequality in general multi-connected domains in R^n2012

    • Author(s)
      H. Kozono, R. Farwig, T. Yanagisawa
    • Journal Title

      Mathematische Annalen(online first)

      Volume: 354 Issue: 1 Pages: 137-145

    • DOI

      10.1007/s00208-011-0716-6

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 多重連結領域における定常Navier-Stokes方程式の境界値問題,研究集会PPM2010報告集偏微分方程式と現象2011

    • Author(s)
      柳沢卓
    • Journal Title

      PDEs and Phenomena in Miyazaki 2010

      Volume: 1

    • Related Report
      2011 Final Research Report
  • [Journal Article] 多重連結領域における定常Navier-Stokes方程式の境界値問題2011

    • Author(s)
      柳沢卓
    • Journal Title

      研究集会PPM2010報告集偏微分方程式と現象:PDEs and Phenomena in Miyazaki 2010

      Volume: 1

    • Related Report
      2011 Annual Research Report
  • [Journal Article] 多重連結領域における定常Navier-Stokes方程式の境界値問題2011

    • Author(s)
      柳沢卓
    • Journal Title

      PDEs and Phenomena in Miyazaki 2010報告集

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Leray's inequality in general multi-connected domains in R^n2011

    • Author(s)
      H.Kozono
    • Journal Title

      Math.Ann.

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analyticity for higher order nonlinear dispersive equations2010

    • Author(s)
      N. Hayashi, K. Tomoeda, T. Yanagisawa
    • Journal Title

      GAKUTO Internat. Ser. Math. Sci. Appl.

      Volume: Vol.32 Pages: 111-130

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Analyticity for higher order nonlinear disiersive equations2010

    • Author(s)
      N.Hayashi
    • Journal Title

      GAKUTO Internat.Ser.Math.Sci.Appl.

      Volume: 32 Pages: 111-130

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Analyticity for higher order nonlinear dispersive equations2010

    • Author(s)
      N.Hayashi, K.Tomoeda, Tomoeda, T.Yanagisawa
    • Journal Title

      Math.Sci.Appli. 32

      Pages: 111-130

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data2009

    • Author(s)
      H. Kozono, T. Yanagisawa
    • Journal Title

      Math. Z.

      Volume: Vol.262 Pages: 27-39

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] L^r-varitional inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains2009

    • Author(s)
      H. Kozono, T. Yanagisawa
    • Journal Title

      Indiana Univ. Math. J.

      Volume: Vol.58 Pages: 1853-1920

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global DIV-CURL Lemma on bounded domains in R^32009

    • Author(s)
      H. Kozono, T. Yanagisawa
    • Journal Title

      J. Funct. Anal.

      Volume: Vol.256 Pages: 3847-3859

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nonhomogeneous boundary value problems for stationary Navier-Stokes equations in a multiply connected domain2009

    • Author(s)
      H. Kozono, T. Yanagisawa
    • Journal Title

      Pacific J. Math.

      Volume: Vol.243 Pages: 127-150

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global DIV-CURL Lemma in 3D bounded domains2009

    • Author(s)
      H. Kozono, T. Yanagisawa
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B14 Pages: 27-33

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Leray's problem on the stationary Navier-Stokes equations with inhomogeneous bounadary data2009

    • Author(s)
      H.Kozono, T.Yanagisawa
    • Journal Title

      Math.Z. 262

      Pages: 27-39

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] L^r-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains2009

    • Author(s)
      H.Kozono, T.Yanagisawa
    • Journal Title

      Indiana Univ.Math.J. 58

      Pages: 1853-1920

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global DIV-CURL Lemma on bounded domains in R^32009

    • Author(s)
      H.Kozono, T.Yanagisawa
    • Journal Title

      J.Funct.Anal. 256

      Pages: 3847-3859

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Nonhomogeneous boundary value problems for stationary Navier-Stokes equations in a multiply connected domain2009

    • Author(s)
      H.Kozono, T.Yanagisawa
    • Journal Title

      Pacific J.Math. 243

      Pages: 127-150

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global DIV-CURL Lemma in 3D bounded domains2009

    • Author(s)
      H.Kozono, T.Yanagisawa
    • Journal Title

      RIMS Kokyuroku Bessatsu B14 14

      Pages: 27-33

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] On global compensated compactness theorem2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      International Conference on Fluid and Gas Dynamics(招待講演)
    • Place of Presentation
      Jinhua, China
    • Year and Date
      2011-09-25
    • Related Report
      2011 Final Research Report
  • [Presentation] On global compensated compactness theorem2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      International Conference on Fluid and Gas Dynamics
    • Place of Presentation
      金華市,中国(招待講演)
    • Year and Date
      2011-09-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] Applications of Hodge decomposition to mathematical fluid Dynamics, The 4th MSJ-SI : Nonlinear Dynamics in Partial Different ial Equations2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      日本数学会,(招待講演)
    • Place of Presentation
      九州大学医学部記念講堂,福岡市
    • Year and Date
      2011-09-19
    • Related Report
      2011 Final Research Report
  • [Presentation] Applications of Hodge decomposition to mathematical fluid dynamics2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      The 4th MSJ-SI : Nonlinear Dynamics in Partial Differential Equations,日本数学会
    • Place of Presentation
      九州大学医学部記念講堂,博多(招待講演)
    • Year and Date
      2011-09-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] Boundary value problems of the stationary MHD equations and Navier-Stokes equations with Coriolis force2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      Partial Differential Equations in Mathematical Physics and their Numerical Approximation(招待講演)
    • Place of Presentation
      Levico Terme(Trento), Italy
    • Year and Date
      2011-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] Boundary value problems of the stationary MHD equations and Navier-Stokes equations with Coriolis force2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      PartialDifferential Equations in Mathematical Physics and their Numerical Approximation
    • Place of Presentation
      Levico Terme (Trento), Italy(招待講演)
    • Year and Date
      2011-09-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] On the stationary boundary value problems of the Navier-Stokes equations with in and out flow on the boundary2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      7th International Congress on Industrial and Applied Mathematics(招待講演)
    • Place of Presentation
      Vancouver Convention Center, Canada
    • Year and Date
      2011-07-18
    • Related Report
      2011 Final Research Report
  • [Presentation] On the stationary boundary value problems of the Navier-Stokes equations with in and out flow on the boundary2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      7th Internatinal Congress on Industrial and Applied Mathematics
    • Place of Presentation
      Vancouver, Convention Center, Canada(招待講演)
    • Year and Date
      2011-07-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] The solvability of stationary Navier-Stokes equations with inhomogeneous boundary data2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      International Conference on Mathematical Fluid Mechanics and Biomedical Applications(招待講演)
    • Place of Presentation
      Univ. of Ponta Delgada, Azores, Portugal
    • Year and Date
      2011-06-03
    • Related Report
      2011 Final Research Report
  • [Presentation] The solvability of stationary Navier-Stokes equations with inhomogeneous boundary data2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      International Conference on Mathematical Fluid Mechanics and Biomedical Applications
    • Place of Presentation
      Univ.of Ponta Delgada, Portugal(招待講演)
    • Year and Date
      2011-06-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] The stationary Navier-Stokes equations under the inhomogeneous boundary conditions2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      International Workshop on Interaction between Mathematics and Fluid Mechanics
    • Place of Presentation
      大阪大学(吹田市)
    • Year and Date
      2011-03-08
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] On global compensated compactness theorem2011

    • Author(s)
      Taku Yanagisawa
    • Organizer
      The 3^<rd> Nagoya Workshop on Differential Equations(招待講演)
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2011-02-14
    • Related Report
      2011 Final Research Report
  • [Presentation] On global compensated compactness theorem2011

    • Author(s)
      柳沢卓
    • Organizer
      The 3^<rd> Nagoya Workshop on Differential Equations
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2011-02-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] 多重連結領域における定常Navier-Stokes方程式の境界値問題2010

    • Author(s)
      柳沢卓
    • Organizer
      PDEs and Phenomena in Miyazaki 2010(招待講演)
    • Place of Presentation
      宮崎大学(宮崎市)
    • Year and Date
      2010-11-21
    • Related Report
      2011 Final Research Report
  • [Presentation] 多重連結領域における定常Navier-Stokes方程式の境界値問題2010

    • Author(s)
      柳沢卓
    • Organizer
      PDEs and Phenomena in Miyazaki 2010
    • Place of Presentation
      宮崎大学(宮崎市)
    • Year and Date
      2010-11-21
    • Related Report
      2010 Annual Research Report
  • [Presentation] Global compensated compactness theorem2010

    • Author(s)
      Taku Yanagisawa
    • Organizer
      Partial Diffe-rential Equations and Mathematical Physics(招待講演)
    • Place of Presentation
      芝蘭会館(京都市)
    • Year and Date
      2010-11-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Global compensated compactness theorem2010

    • Author(s)
      柳沢卓
    • Organizer
      Partial Differential Equations and Mathematical Physics
    • Place of Presentation
      芝蘭会館(京都市)
    • Year and Date
      2010-11-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] 調和ベクトル場と流体力学等に現れる定常解2010

    • Author(s)
      柳沢卓
    • Organizer
      青葉山勉強会(第5回)(招待講演)
    • Place of Presentation
      東北大学情報科学研究科(仙台市)
    • Year and Date
      2010-06-11
    • Related Report
      2011 Final Research Report
  • [Presentation] 調和ベクトル場と流体力学等に現れる定常解2010

    • Author(s)
      柳沢卓
    • Organizer
      青葉山勉強会(第5回)
    • Place of Presentation
      東北大学情報科学研究科(仙台市)
    • Year and Date
      2010-06-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] ベクトル場の分解定理とその流体力学への応用2010

    • Author(s)
      柳沢卓
    • Organizer
      乱流場と非線形構造-数学と流体力学の融合を目指して-(招待講演)
    • Place of Presentation
      東北大学数理科学記念館(仙台市)
    • Year and Date
      2010-04-24
    • Related Report
      2011 Final Research Report
  • [Presentation] ベクトル場の分解定理とその流体力学への応用2010

    • Author(s)
      柳沢卓
    • Organizer
      乱流場と非線形構造-数学と流体力学の融合を目指して-
    • Place of Presentation
      東北大学数理科学記念館(仙台市)
    • Year and Date
      2010-04-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] Helmholtz-Weyl分解とその応用2010

    • Author(s)
      柳沢卓
    • Organizer
      日本数学会2010年度年会函数方程式論分科会特別講演(招待講演)
    • Place of Presentation
      慶応義塾大学,横浜市
    • Year and Date
      2010-03-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Helmholtz-Weyl分解とその応用2010

    • Author(s)
      柳沢卓
    • Organizer
      日本数学会2010年度年会函数方程式論分科会特別講演
    • Place of Presentation
      慶応義塾大学,横浜市
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 境界層方程式について2009

    • Author(s)
      柳沢卓
    • Organizer
      第2回CESセミナー
    • Place of Presentation
      早稲田大学,東京都新宿区
    • Year and Date
      2009-11-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] Asymptotic behavior of solutions to the viscous Burgers equation2009

    • Author(s)
      Taku Yanagisawa
    • Organizer
      Linear and Nonlinear Waves,(招待講演)
    • Place of Presentation
      大津市
    • Year and Date
      2009-11-05
    • Related Report
      2011 Final Research Report
  • [Presentation] Asymptotic behavior of solutions to the viscous Burgers equation2009

    • Author(s)
      柳沢卓
    • Organizer
      Linear and Nonlinear Waves, No.7
    • Place of Presentation
      大津市
    • Year and Date
      2009-11-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the stationary Navier-Stokes equations in a 3D bounded domain under the nonhomogeneous boundary condition2009

    • Author(s)
      Taku Yanagisawa
    • Organizer
      Conference on "Mathematical Physics and PDEs(招待講演)
    • Place of Presentation
      Levico Terme, Trento, Italy
    • Year and Date
      2009-09-08
    • Related Report
      2011 Final Research Report
  • [Presentation] On the stationary Navier-Stokes equations in a 3D bounded domain under the nonhomogeneous boundary condition2009

    • Author(s)
      柳沢卓
    • Organizer
      Conference on "Mathematical Physics and PDEs
    • Place of Presentation
      Levico Terme, Trento, Italy
    • Year and Date
      2009-09-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data II2009

    • Author(s)
      柳沢卓
    • Organizer
      PDE seminar at Zhejiang Normal University
    • Place of Presentation
      Jinhua, China
    • Year and Date
      2009-05-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Leray's inequality in 3D domains2009

    • Author(s)
      柳沢卓
    • Organizer
      PDE seminar at Zhejiang Normal University
    • Place of Presentation
      Jinhua, China
    • Year and Date
      2009-05-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I2009

    • Author(s)
      柳沢卓
    • Organizer
      PDE seminar at Zhejiang Normal University
    • Place of Presentation
      Jinhua, China
    • Year and Date
      2009-05-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] Blow-up criteria for smooth solutions of 3-D compressible Euler equations on a bounded domain2009

    • Author(s)
      Taku Yanagisawa
    • Organizer
      Topics of Fluid Dynamics(招待講演)
    • Place of Presentation
      Brescia University, Brescia, Italy
    • Year and Date
      2009-04-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Blow-up criteria for smooth solutions of 3-D compressible Euler equations on a bounded domain2009

    • Author(s)
      柳沢卓
    • Organizer
      Topics of Fluid Dynamics
    • Place of Presentation
      Brescia University, Brescia, Italy
    • Year and Date
      2009-04-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] (Part I) Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data I,(Part II) Leray's problems on the stationary Navier-Stokes equations with inhomogeneous boundary data II,(Part III) Leray's inequality in 3D domains2009

    • Author(s)
      Taku Yanagisawa
    • Organizer
      PDE seminar at Zhejiang Normal university(連続招待講演)
    • Place of Presentation
      Jinhua, China
    • Related Report
      2011 Final Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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