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非有界領域上における圧縮性流体方程式の時間周期問題

Research Project

Project/Area Number 17J04778
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section国内
Research Field Mathematical analysis
Research InstitutionOsaka University

Principal Investigator

津田 和幸  大阪大学, 基礎工学研究科, 特別研究員(PD)

Project Period (FY) 2017-04-26 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
KeywordsNavier-Stokes-Kortweg方程式 / 臨界条件 / diffusion wave / 2.非圧縮性Navier-Stokes方程式 / 時間周期問題 / 流体方程式 / 臨界条件下 / 最大正則性定理 / 圧縮性流体方程式 / 解の時間減衰評価
Outline of Annual Research Achievements

私の研究分野は非線形偏微分方程式の数学解析である. これまでに流体力学の基礎方程式である圧縮性および非圧縮性Navier-Stokes方程式の研究を行ってきた. これらの方程式系は, 解の存在, 一意性, 正則性, 安定性や漸近挙動などの偏微分方程式論におけるさまざま基本的課題を提供してきた方程式系であり, 豊かな数学的構造を備え,多様な物理学・工学的応用を有している. 私は非有界領域における圧縮性流体方程式の時間周期問題を主な研究課題とし, 今年度は以下のような成果を発表した.
受け入れ研究者である小林孝行教授との共同研究により, 初期値に適当な正則性の仮定を課したもと, 臨界条件下において小さい初期値に対する時間大域解の存在と解の定数状態への収束率を導出した. この収束率は熱方程式の解と同じ減衰率であることも明らかにした. またスペクトルの挙動から, 線形化方程式の解について, パラメータの値によって純粋な粘性拡散の場合と, 粘性拡散に加えて分散性も出現することを明らかにした.
小林孝行教授と熊本大学の三沢正史との共同研究により, 全空間上での圧縮性Navier-Stokes-Kortweg方程式の拡散波について, 特殊な初期値を取ったとき, 拡散波である流体の密度が放物型と同じ減衰をし, さらに解のモーメントの拡散波部分が密度より遅く減衰することを明らかにした.
ドイツ・Darmstadt工科大学のFarwig教授に招待され, 2019年5月~7月まで同大学に滞在して研究活動を行った. 非圧縮性Navier-Stokes方程式の, 境界が周期的に動く有界領域での時間周期問題に関する研究を行った.時間周期的移動境界問題を考察し,スケール保存則を含むL^pクラスにおいて時間周期解を構成することに成功した.

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (31 results)

All 2020 2019 2018 2017 Other

All Int'l Joint Research (5 results) Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results,  Open Access: 2 results) Presentation (18 results) (of which Int'l Joint Research: 10 results,  Invited: 4 results)

  • [Int'l Joint Research] Technische Universit at Darmstadt/Reinhard Farwig教授(ドイツ)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 首都師範大学/Hailiang Li教授(中国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] ダルムシュタット工科大学/R. Farwig教授(ドイツ)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] 首都師範大学/H. Li 教授(中国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] Peking University(China)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] Global existence and time decay estimate of solutions to the compressible two phase flow system under critical condition2020

    • Author(s)
      Kobayashi Takayuki and Kazuyuki Tsuda
    • Journal Title

      Asymptotic Analysis

      Volume: -

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] The Time Periodic Problem of the Navier-Stokes Equations in a Bounded Domain with Moving Boundary2020

    • Author(s)
      Reinhard Farwig, Hideo Kozono, Kazuyuki Tsuda, and David Wegmann
    • Journal Title

      preprint

      Volume: -

    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Journal Article] Asymptotic profile for diffusion wave terms of the compressible Navier-Stokes-Korteweg system2019

    • Author(s)
      Takayuki Kobayashi, Masashi Misawa and Kazuyuki Tsuda
    • Journal Title

      Preprint, arXiv:1907.04682

      Volume: -

    • Related Report
      2019 Annual Research Report
  • [Journal Article] Time decay estimate with diffusive property and smoothing effect for solution to the compressible Navier-Stokes-Korteweg system2019

    • Author(s)
      Takayuki Kobayashi and Kazuyuki Tsuda
    • Journal Title

      The FUNKCIALAJ EKVACIO, 掲載受理

      Volume: 掲載受理

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] “Global existence and time decay estimate of solutions to the compressible two phase flow system under critical condition2019

    • Author(s)
      Kobayashi Takayuki and Kazuyuki Tsuda
    • Journal Title

      投稿中

      Volume: 投稿中

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Asymptotic profile for diffusion wave terms of the compressible Navier-Stokes-Korteweg system2019

    • Author(s)
      Takayuki Kobayashi, Masashi Misawa and Kazuyuki Tsuda
    • Journal Title

      preprint

      Volume: preprint

    • Related Report
      2018 Annual Research Report
  • [Journal Article] The Time Periodic Problem of the Navier-Stokes Equations in a Bounded Domain with Moving Boundary in Maximal Regularity Classes2019

    • Author(s)
      Reinhard Farwig, Hideo Kozono, Kazuyuki Tsuda and David Wegmann
    • Journal Title

      preprint

      Volume: preprint

    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Journal Article] Time periodic problem for the compressible Navier–Stokes equation on ℝ<sup>2</sup> with antisymmetry2018

    • Author(s)
      Kazuyuki Tsuda
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 70 Issue: 1 Pages: 243-281

    • DOI

      10.2969/jmsj/07017524

    • NAID

      130006334071

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] The Time Periodic Problem of the Navier-Stokes Equations in a Bounded Domain with Moving Boundary2020

    • Author(s)
      Reinhard Farwig, Hideo Kozono, Kazuyuki Tsuda, and David Wegmann
    • Organizer
      日本数学会2020年度年会
    • Related Report
      2019 Annual Research Report
  • [Presentation] The Time Periodic Problem of the Navier-Stokes Equations in a Bounded Domain with Moving Boundary2020

    • Author(s)
      Reinhard Farwig, Hideo Kozono, Kazuyuki Tsuda, and David Wegmann
    • Organizer
      大阪大学微分方程式セミナー
    • Related Report
      2019 Annual Research Report
  • [Presentation] Global Existence and Time Decay Estimate of Solutions to the CompressibleNavier-Stokes-Korteweg System Under Critical Condition2019

    • Author(s)
      Kobayashi Takayuki and Kazuyuki Tsuda
    • Organizer
      The 7th China-Japan Workshop on Mathematical Topics from Fluid Mechanics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Time decay estimate with diffusion wave property and smoothing effect for solutions to the compressible Navier-Stokes-Korteweg system2019

    • Author(s)
      Kobayashi Takayuki and Kazuyuki Tsuda
    • Organizer
      Seminar talk in Beijing University of Chemical Technology
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Global Existence and Time Decay Estimate of Solutions to the Compressible Navier-Stokes-Korteweg System Under Critical Condition2019

    • Author(s)
      Kobayashi Takayuki and Kazuyuki Tsuda
    • Organizer
      Oberseminor Analysis, Technische Universit at Darmstadt
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] On the global existence and time decay estimate of solutions to the compressible Navier-StokesKorteweg system2019

    • Author(s)
      津田 和幸
    • Organizer
      若手による流体力学の基礎方程式研究集会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Global existence and time decay estimate of solutions to the compressible two phase flow system under critical condition2019

    • Author(s)
      小林 孝行、津田 和幸
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 圧縮性Navier-Stokes-Korteweg方程式の解の時間減衰評価について2018

    • Author(s)
      津田 和幸
    • Organizer
      南大阪応用数学セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] Diffusion wave property and smoothing effect for solution to the compressible Navier-Stokes-Korteweg system2018

    • Author(s)
      津田 和幸
    • Organizer
      熊本大学応用解析セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] Diffusion wave property and smoothing effect for solution to the compressible Navier-Stokes-Korteweg system2018

    • Author(s)
      津田 和幸
    • Organizer
      第40回発展方程式若手セミナー
    • Related Report
      2018 Annual Research Report
  • [Presentation] Time decay estimate including diffusive wave property for solution to the compressible Navier-Stokes-Korteweg system2018

    • Author(s)
      津田 和幸
    • Organizer
      Ito Workshop on Partial Differential Equations
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Diffusive wave property and smoothing effect for solution to the compressible Navier-Stokes-Korteweg equation2018

    • Author(s)
      Kazuyuki Tsuda
    • Organizer
      The 15th Japanese-German International Workshop on Mathematical Fluid Dynamics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 全空間上の圧縮性Navier-Stokes方程式の時間周期問題について2017

    • Author(s)
      津田和幸
    • Organizer
      第6回岐阜数理科学研究会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Time periodic problem for the compressible Navier-Stokes equation on two-dimensional whole space2017

    • Author(s)
      Kazuyuki Tsuda
    • Organizer
      Nonlinear Partial Differential Equations for Future Applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Time periodic problem for the compressible Navier-Stokes equation on the whole space2017

    • Author(s)
      Kazuyuki Tsuda
    • Organizer
      The sixth Japan-China Workshop on Mathematical Topics from Fluid Mechanics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Time decay estimate with diffusive property and smoothing effect for solution to the compressible Navier-Stokes-Korteweg system2017

    • Author(s)
      Kazuyuki Tsuda
    • Organizer
      International Workshop on the Multi-Phase Flow; Analysis, Modelling and Numerics
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Diffusive wave property and smoothing effect for solution to the compressible Navier-Stokes-Korteweg system2017

    • Author(s)
      Kazuyuki Tsuda
    • Organizer
      2017 PNU Math Forum
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Time periodic problem for the compressible Navier-Stokes equation on the two dimensional whole space with antisymmetry2017

    • Author(s)
      Kazuyuki Tsuda
    • Organizer
      2017 Taiwan-Japan Workshop on Dispersion, Navier Stokes, Kinetic, and Inverse Problems
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited

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Published: 2017-05-25   Modified: 2024-03-26  

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