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Solvability and asymptotic behavior of solution for stochastic nonlinear dispersive equations

Research Project

Project/Area Number 23654051
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionKyoto University

Principal Investigator

TSUTSUMI YOSHIO  京都大学, 理学(系)研究科(研究院), 教授 (10180027)

Research Collaborator BOUARD Anne De  パリ理工科学校
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords確率非線形分散型方程式 / Gibbs測度 / Kuksin流の不変測度 / 等温Falkモデル / 加法的ノイズ付きZkharov方程式 / 電離層における電磁場擾乱 / 時間大域解の存在 / Kuksinの不変測度 / 解のア・プリオリ評価 / 確率Zakharov方程式 / 時間大域解 / 非線形分散型方程式 / 不変測度 / Falkモデル方程式 / 初期値問題の可解性 / ノイズによる正則化 / ノイズによる安定化 / 拡散極限
Research Abstract

If the scale or the measure is appropriately chosen, the volume of flows generated by evolution equations can be conserved. Such a measure is called an invariant measure. It is very important to construct an invariant measure, because the global behavior of solutions for nonlinear evolution equations can be investigated in view of the invariant measure. We have constructed two kinds of invariant measures, that is, the Gibbs measure and the measure proposed by Kuksin. We also have copared those two invariantmeasures. Furthermore, we have studied the Zakharov equations with additive noises, which is a mathematical model to describe a turbulence of spectrums of electromagnetic waves in the ionosphere. We have proved the global existence in time of solutions for the Cauchy problem of the Zakharove equations with additive noises.

Report

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

    (12 results)

All 2014 2013 2012 2011 Other

All Journal Article (4 results) (of which Peer Reviewed: 2 results) Presentation (8 results) (of which Invited: 7 results)

  • [Journal Article] Invariant measures for the isothermal Falk model of shape memory alloys2014

    • Author(s)
      Yoshio Tsutsumi and Shuji Yoshikawa
    • Journal Title

      Mathematical Sciences and Applications

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 1D quantic nonlinear Schrödinger with white noise dispersion2011

    • Author(s)
      Arnaud Debussche and Yoshio Tsutsumi
    • Journal Title

      Journal de Mathématiques Pures et Appliquées

      Volume: 96 Pages: 363-376

    • Related Report
      2013 Final Research Report
  • [Journal Article] 1D quintic nonlinear Schrodinger equation with white noise dispersion2011

    • Author(s)
      Arnaud Debussche and Yoshio Tsutsumi
    • Journal Title

      J. Math. Pures Appl.

      Volume: 96 Issue: 4 Pages: 363-376

    • DOI

      10.1016/j.matpur.2011.02.002

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Inavariant measures for the isothermal Falk model of shape memory alloys

    • Author(s)
      Yoshio Tsutsumi and Shuji Yoshikawa
    • Journal Title

      Mathematical Sciences and Applications

      Volume: (to appear)

    • Related Report
      2013 Final Research Report
  • [Presentation] Global existence of solutions for 1D Zakharov equations with additive noises2013

    • Author(s)
      Yoshio Tsutsumi
    • Organizer
      International Workshop on Differential Equations and its Applications
    • Place of Presentation
      台湾, 国立成功大学
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Global L^2 solutions of 1D Zakharov equations with additive noises2013

    • Author(s)
      Yoshio Tsutsumi
    • Organizer
      保存則を持つ偏微分方程式に対する解の正則性・特異性の研究
    • Place of Presentation
      京都大学数理解析研究所, 京都
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Global existence of solutions for 1D Zakharov equations with additive noises2013

    • Author(s)
      Yoshio Tsutsumi
    • Organizer
      International Workshop on Differential Equations and its Applications
    • Place of Presentation
      国立成功大学,台湾台南
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Global L^2 solutions of 1D Zakharov equations with additive noises2013

    • Author(s)
      Yoshio Tsutsumi
    • Organizer
      保存則を持つ偏微分方程式に対する解の正則性・特異性の研究
    • Place of Presentation
      京都大学数理解析研究所,京都
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Parabolic-stochastic regularization for H^1 critical NLS2012

    • Author(s)
      堤 誉志雄
    • Organizer
      奈良女子大学偏微分方程式研究集会
    • Place of Presentation
      奈良女子大学,奈良
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Gibbs measure for the isothermal Falk mode2012

    • Author(s)
      Yoshio Tsutsumi
    • Organizer
      Mathematical Fluid Dynamics and Nonlinear Wave
    • Place of Presentation
      Waseda University, Tokyo
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Gibbs measure for isothermal Falk model2012

    • Author(s)
      Yoshio Tsutsumi
    • Organizer
      Parabolic and Navier-Stokes Equations
    • Place of Presentation
      Mathematical Research and Conference Center, Bedlewo
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 1D quintic nonlinear Schrodinger equation wit white noise dispersion2011

    • Author(s)
      堤誉志雄
    • Organizer
      偏微分方程式の背後にある確率過程と解の族が示す統計力学的現象の解析(招待講演)
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report

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

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