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Asymptotic analysis of spherical solution of compressible viscous fluid

Research Project

Project/Area Number 17K14227
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionKanazawa University (2019-2020)
Kansai University (2018)
Osaka City University (2017)

Principal Investigator

Kai Itsuko  金沢大学, 機械工学系, 准教授 (70584639)

Project Period (FY) 2017-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords外部問題 / 球対称問題 / 偏微分方程式論 / 圧縮性 / ナビエ-ストークス方程式 / 外部問題の数学解析 / 保存則 / ナビエ・ストークス方程式 / バーガーズ方程式 / 単独粘性保存則 / 関数方程式 / 圧縮性粘性流体 / 漸近安定性 / 関数方程式論
Outline of Final Research Achievements

We considered the asymptotic behaviors of radially symmetric solutions for the multi-dimensional Burgers equation on the exterior domain. We found the stationary solution which does not appear on the one simensional space. We used maximum principle, Banach fixed-point theorem and weighted energy method. We recently apply the results of Burgers equation to the radially symmetric stationary solutions for exterior problems to the compressible Navier-Stokes equation, describing the motion of viscous barotropic gas.

Academic Significance and Societal Importance of the Research Achievements

従来の研究においては,1次元バーガーズ方程式の解と高次元球対称バーガーズ方程式の解の挙動は同じものであると考えられてきた.しかしながら,私の研究を通して双方の解の漸近挙動は大きくことなるものであることを発見した.ナビエ-ス-トークスは非圧縮の場合がミレニアム問題として挙げられるほど重要な問題となっており,圧縮性の場合も同様に重要である.バーガーズ方程式は圧縮性ナビエス-トークス方程式の密度を一定とおいて得られる運動方程式である.これまでのバーガーズ方程式で得られた知見はナビエ-ストークス方程式の球対称解の解明へ応用する際に非常に重要である.

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (7 results)

All 2019 2018 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (5 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results) Remarks (1 results)

  • [Journal Article] Asymptotic behavior toward nonlinear waves for radially symmetric solutions of the multi-dimensional Burgers equation2019

    • Author(s)
      Itsuko Hashimoto, Akitaka Matsumura
    • Journal Title

      Journal of sifferential equations

      Volume: 266 Pages: 2805-2829

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] Asymptotic behavior of radially symmetric solutions for the Burgers equation in several space dimensions2019

    • Author(s)
      Itsuko Hashimoto
    • Organizer
      The seventhJapan-China Workshop on Mathematical Topics from Fluid Mechanics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] asymptotic stability of radially symmetric solutions of multi dimensional Burgers equation2019

    • Author(s)
      Itsuko Hashimoto
    • Organizer
      Equadiff 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] バーガーズ方程式の球対称定常解の漸近安定性について2019

    • Author(s)
      橋本伊都子
    • Organizer
      大阪大学微分方程式セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 高次元空間上におけるバーガーズ方程式 の球対称定常波の安定性2019

    • Author(s)
      橋本伊都子
    • Organizer
      日本数学会 年度会
    • Related Report
      2018 Research-status Report
  • [Presentation] 多次元空間上におけるバーガース方程式の 球対称問題の漸近挙動について2018

    • Author(s)
      橋本伊都子, 松村昭孝
    • Organizer
      日本数学会年会
    • Related Report
      2017 Research-status Report
  • [Remarks] 橋本伊都子

    • URL

      https://researchmap.jp/i-hashimoto/

    • Related Report
      2017 Research-status Report

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Published: 2017-04-28   Modified: 2022-01-27  

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