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Large time behavior of the solutions to the equations of fluid motion.

Research Project

Project/Area Number 23540211
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionEhime University

Principal Investigator

YANAGI Shigenori  愛媛大学, 理工学研究科, 准教授 (10253296)

Co-Investigator(Kenkyū-buntansha) NAKAMURA Tohru  九州大学, 大学院数理学研究院, 助教 (90432898)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
KeywordsNavier-Stokes 方程式 / 圧縮性流体 / 時間大域的挙動 / Navier-Stokes方程式
Research Abstract

In the present research, we consider the nonlinear symmetric systems of hyperbolic and parabolic type which describe the motion of compressible and viscous fluids. For this system, we show the existence and asymptotic stability of stationary waves in a half space. We show that the condition for the existence of stationary waves is characterized by the number of negative characteristics. We also prove the asymptotic stability of the stationary waves in a suitable Sobolev space by using the energy method under the stability condition of Shizuta-Kawashima type.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (25 results)

All 2014 2013 2012 2011 Other

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (15 results) (of which Invited: 7 results)

  • [Journal Article] Energy estimate for a linear symmetric hyperbolic-parabolic system in half line2013

    • Author(s)
      T. Nakamura and S. Nishibata
    • Journal Title

      Kinet. Relat. Models

      Volume: 6 Pages: 883-892

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy estimate for a linear symmetric hyperbolic-parabolic system in half line2013

    • Author(s)
      T. Nakamura and S. Nishibata
    • Journal Title

      Kinet. Relat. Models

      Volume: 6 Issue: 4 Pages: 883-892

    • DOI

      10.3934/krm.2013.6.883

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay estimates of solutions for quasi-linear hyperbolic systems of viscoelasticity2012

    • Author(s)
      P. M. N.Dharmawardane, T. Nakamura and S. Kawashima
    • Journal Title

      SIAM J. Math. Anal

      Volume: 44 Pages: 1976-2001

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Decay estimates of solutions for quasi-linear hyperbolic systems of viscoelasticity2012

    • Author(s)
      P.M.N. Dharmawardane
    • Journal Title

      SIAM J. Math. Anal.

      Volume: 44 Issue: 3 Pages: 1976-2001

    • DOI

      10.1137/11083900x

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas2011

    • Author(s)
      T. Nakamura and S. Nishibata
    • Journal Title

      J. Hyperbolic Differ. Equ

      Volume: 8 Pages: 651-670

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solutions to quasi-linear hyperbolic systems of viscoelasticity2011

    • Author(s)
      P. M. N. Dharmawardane, T. Nakamura and S. Kawashima
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 51 Pages: 467-483

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy method in the partial Fourier space and application to stability problems in the half space2011

    • Author(s)
      Y. Ueda, T. Nakamura and S. Kawashima
    • Journal Title

      J. Differential Equations

      Volume: 250 Pages: 1169-1199

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stationary wave associated with an inflow problem in the half line for viscous heat-conductive gas2011

    • Author(s)
      T.Nakamura, et al
    • Journal Title

      Journal of Hyperbolic Differential Equations

      Volume: 8 Issue: 04 Pages: 651-670

    • DOI

      10.1142/s0219891611002524

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global solutions to quasi-linear hyperbolic systems of viscoelasticity2011

    • Author(s)
      P.M.N.Dharmawardane
    • Journal Title

      Kyoto J.Math.

      Volume: 51 Issue: 2 Pages: 467-483

    • DOI

      10.1215/21562261-1214411

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Energy method in the partial Fourier space and application to stability problems in the half space.2011

    • Author(s)
      Y. Ueda, T. Nakamura, S. Kawashima
    • Journal Title

      J. Differential Equations

      Volume: 250 Issue: 2 Pages: 1169-1199

    • DOI

      10.1016/j.jde.2010.10.003

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Stationary wave to systems of viscous conservation laws in half line2014

    • Author(s)
      T. Nakamura
    • Organizer
      IMS Workshop on Nonlinear PDEs from Fluids and Related Topics
    • Place of Presentation
      Chinese University of Hong Kong
    • Year and Date
      2014-03-24
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] 消散的な対称双曲放物型連立系に現れる定常波の存在性と漸近安定性2013

    • Author(s)
      中村 徹
    • Organizer
      第11回浜松偏微分方程式研究集会
    • Place of Presentation
      静岡大学
    • Year and Date
      2013-12-24
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] 1 次元対称双曲放物型連立系に現れる境界層解について2013

    • Author(s)
      中村 徹
    • Organizer
      第3回室蘭非線形解析研究会
    • Place of Presentation
      室蘭工業大学
    • Year and Date
      2013-11-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Stationary wave to systems of viscous conservation laws in half line2013

    • Author(s)
      T. Nakamura
    • Organizer
      RIMS Workshop "Kinetic Modeling and Related Equations: Conference in Memory of Seiji Ukai"
    • Place of Presentation
      京都大学
    • Year and Date
      2013-10-29
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Boundary layer solution to system of viscous conservation laws in half line2013

    • Author(s)
      T. Nakamura
    • Organizer
      研究集会「第9回非線型の諸問題」
    • Place of Presentation
      高知大学
    • Year and Date
      2013-09-05
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Invited
  • [Presentation] Boundary layer solution to the symmetric hyperbolic-parabolic system2012

    • Author(s)
      T. Nakamura
    • Organizer
      The 7th Japanese--German International Workshop on Mathematical Fluid Dynamics
    • Place of Presentation
      早稲田大学
    • Year and Date
      2012-11-08
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Boundary layer solution to systems of viscous conservation laws in half line2012

    • Author(s)
      T. Nakamura
    • Organizer
      14th International Conference on Hyperbolic Problems: Theory, Numerics, Applications
    • Place of Presentation
      University of Padova, Italy
    • Year and Date
      2012-06-26
    • Related Report
      2013 Final Research Report
  • [Presentation] 半直線上の粘性的保存則系に対する定常解の存在性と漸近安定性2012

    • Author(s)
      中村 徹
    • Organizer
      非線形解析セミナー
    • Place of Presentation
      東京工業大学
    • Year and Date
      2012-05-28
    • Related Report
      2013 Final Research Report 2012 Research-status Report
  • [Presentation] S tationary wave to the symmetric hyperbolic-parabolic system in half space2011

    • Author(s)
      T. Nakamura
    • Organizer
      Analysis of Partial Differential Equations
    • Place of Presentation
      San Diego, California, USA
    • Year and Date
      2011-11-05
    • Related Report
      2013 Final Research Report
  • [Presentation] 熱伝導圧縮性粘性流体に現れる境界層解の存在性と漸近安定性2011

    • Author(s)
      中村 徹
    • Organizer
      日本流体力学会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2011-09-07
    • Related Report
      2013 Final Research Report 2011 Research-status Report
  • [Presentation] Asymptotic stability of stationary waves for symmetric hyperbolic -parabolic system in half space2011

    • Author(s)
      T. Nakamura
    • Organizer
      RIMS 研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学数理科学研究所
    • Year and Date
      2011-07-08
    • Related Report
      2013 Final Research Report
  • [Presentation] Stationary wave to the symmetric hyperbolic-parabolic system in half space2011

    • Author(s)
      T.Nakamura
    • Organizer
      Analysis of Partial Differential Equations
    • Place of Presentation
      San Diego, California, USA
    • Related Report
      2011 Research-status Report
  • [Presentation] Asymptotic stability of stationary waves for symmetric hyperbolic-parabolic system in half space2011

    • Author(s)
      T.Nakamura
    • Organizer
      RIMS研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report
  • [Presentation] Boundary layer solution to the symmetric hyperbolic-parabolic system

    • Author(s)
      T.Nakamura
    • Organizer
      The 7th Japanese--German International Workshop on Mathematical Fluid Dynamics
    • Place of Presentation
      早稲田大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Boundary layer solution to systems of viscous conservation laws in half line

    • Author(s)
      T.Nakamura
    • Organizer
      14th International Conference on Hyperbolic Problems : Theory, Numerics, Applications
    • Place of Presentation
      University of Padova, Italy
    • Related Report
      2012 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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