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Mathematical modeling and analysis of astronomical phenomena on the basis of continuum approximation

Research Project

Project/Area Number 23740099
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionUniversity of Miyazaki (2012-2013)
Ibaraki University (2011)

Principal Investigator

UMEHARA Morimichi  宮崎大学, 工学部, 准教授 (40532164)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
KeywordsNavier-Stokes方程式 / 自由境界問題 / 圧縮性粘性流体 / 自己重力 / 天体の連続体モデル / 球対称運動 / 二相問題 / Stefan問題
Research Abstract

We mathematically modelized, on the basis of continuum approximation, some astrophysical phenomena including the inner one of astronomical bodies, and mathematically analyzed them. We obtained the following main two results: (1) On the case that a star is composed by the ideal gas and its motion is spacially one-dimensional, we found a certain condition, concerning external circumstances of the star, guaranteeing that the motion of the gas exists long-time and stably; (2) On the case that the gaseous motion is spherically symmetric in three-dimension, we obtained the result nearly equivalent to the one in (1). Although a precedent result of our study has already been obtained by the present reporter, we succeeded in refining them at some essential points.

Report

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

    (27 results)

All 2014 2013 2012 2011 Other

All Journal Article (6 results) (of which Peer Reviewed: 2 results) Presentation (17 results) (of which Invited: 1 results) Remarks (4 results)

  • [Journal Article] Free-boundary problem of the equations for flows of viscous heat-conducting and self-gravitating gas2014

    • Author(s)
      M. Umehara
    • Journal Title

      Mathematical analysis in fluid and gas dynamics (The 15^<th> workshop), (edited by T. Kobayashi and T. Iguchi) (RIMS Kokyuroku, 1883, RIMS Kyoto Univ)

      Pages: 75-83

    • Related Report
      2013 Final Research Report
  • [Journal Article] Large-time existence of the spherically symmetric flow of a self-gravitating viscous gas2014

    • Author(s)
      M. Umehara
    • Journal Title

      In : Unified understanding of self-organizations in N-body systems governed by long-range, edited by Y. Yatsuyanagi and H. Ohtsuka (RIMS Kokyuroku, 1885, RIMS Kyoto Univ)

      Pages: 105-115

    • Related Report
      2013 Final Research Report
  • [Journal Article] Large-time existence of the spherically symmetric flow of a self-gravitating viscous gas2014

    • Author(s)
      M. Umehara
    • Journal Title

      数理解析研究所講究録

      Volume: 1885 Pages: 105-115

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Free-boundary problem of the equations for flows of viscous heat- conducting and self-gravitating gas2014

    • Author(s)
      M. Umehara
    • Journal Title

      数理解析研究所講究録

      Volume: 1883 Pages: 75-83

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Free-boundary problem of the one-dimensional equations for a viscous and heat-conductive gaseous flow under the self-gravitation2013

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      Math. Mod. Meth. Appl. Sci

      Volume: 23 Pages: 1377-1419

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Free-boundary problem of the one-dimensional equations for a viscous and heat-conductive gaseous flow under the self-gravitation2013

    • Author(s)
      Morimichi Umehara and Atusi Tani
    • Journal Title

      Mathematical Models and Methods in Applied Sciences

      Volume: 23 Issue: 08 Pages: 1377-1419

    • DOI

      10.1142/s0218202513500127

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 自己重力粘性ガスの時間大域的な運動について2013

    • Author(s)
      梅原守道
    • Organizer
      第3回弘前非線形方程式研究会
    • Place of Presentation
      弘前大学
    • Year and Date
      2013-11-18
    • Related Report
      2013 Final Research Report
  • [Presentation] 星の脈動の方程式について2013

    • Author(s)
      梅原守道
    • Organizer
      現象解析特別セミナー第4回
    • Place of Presentation
      東京理科大学
    • Year and Date
      2013-09-28
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] Free-boundary problem of the equations for flows of viscous heat-conducting and self-gravitating gas2013

    • Author(s)
      M. Umehara
    • Organizer
      RIMS workshop on Mathematical analysis in fluid and gas dynamics (The 15th workshop)
    • Place of Presentation
      RIMS Kyoto Univ., Japan
    • Year and Date
      2013-07-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Large-time existence of the spherically symmmetric flow of a self-gravitating viscous gas2013

    • Author(s)
      梅原守道
    • Organizer
      RIMS共同研究 : 長距離力に支配された多体系自己組織化の統一的理解を目指して
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-06-21
    • Related Report
      2013 Final Research Report
  • [Presentation] On a spherically symmetric motion of a self-gravitating viscous gas2012

    • Author(s)
      M. Umehara
    • Organizer
      Parabolic and Navier-Stokes Equations 2012, Palac Bedlewo (Institute of mathematics of the Polish academy of sciences)
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2012-09-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Spherically symmetric flow of the self-gravitating viscous gas over the rigid core2011

    • Author(s)
      M. Umehara
    • Organizer
      Third China-Japan workshop on mathematical topics from fluid mechanics
    • Place of Presentation
      Northwest Univ., Xi'an, China
    • Year and Date
      2011-10-25
    • Related Report
      2013 Final Research Report
  • [Presentation] Global existence of the spherically symmetric motion of a self-gravitating viscous gas over the rigid core2011

    • Author(s)
      梅原守道
    • Organizer
      第7回非線型の諸問題
    • Place of Presentation
      熊本大学
    • Year and Date
      2011-09-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Global existence of the spherically symmetric flow of a self-gravitating viscous gas2011

    • Author(s)
      M. Umehara
    • Organizer
      The 4th MSJ-SI Nonlinear dynamics in partial differential equations (in contributed talks)
    • Place of Presentation
      Kyushu Univ., Japan
    • Year and Date
      2011-09-20
    • Related Report
      2013 Final Research Report
  • [Presentation] 自己重力粘性ガスの球対称な流れの長時間存在2011

    • Author(s)
      梅原守道
    • Organizer
      日本流体力学会年会2011
    • Place of Presentation
      首都大学東京
    • Year and Date
      2011-09-07
    • Related Report
      2013 Final Research Report
  • [Presentation] 自己重力粘性ガスの球対称な流れの長時間存在2011

    • Author(s)
      梅原守道
    • Organizer
      日本流体力学会 年会2011
    • Place of Presentation
      首都大学東京
    • Related Report
      2011 Research-status Report
  • [Presentation] Global existence of the spherically symmetric flow of a self-gravitating viscous gas2011

    • Author(s)
      Morimichi Umehara
    • Organizer
      The 4th MSJ-SI Nonlinear dynamics in partial differential equations
    • Place of Presentation
      九州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Global existence of the spherically symmetric motion of a self-gravitating viscous gas over the rigid core2011

    • Author(s)
      梅原守道
    • Organizer
      第7回 非線型の諸問題(招待講演)
    • Place of Presentation
      熊本大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Spherically symmetric flow of the self-gravitating viscous gas over the rigid core2011

    • Author(s)
      Morimichi Umehara
    • Organizer
      Third China-Japan workshop on mathematical topics from fluid mechanics(招待講演)
    • Place of Presentation
      西北大学(西安)
    • Related Report
      2011 Research-status Report
  • [Presentation] Large-time existence of the spherically symmmetric flow of a self-gravitating viscous gas

    • Author(s)
      梅原守道
    • Organizer
      RIMS共同研究:長距離力に支配された多体系自己組織化の統一的理解 を目指して
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Free-boundary problem of the equations for flows of viscous heat-conducting and self-gravitating gas

    • Author(s)
      M. Umehara
    • Organizer
      Mathematical analysis in fluid and gas dynamics (The 15th workshop)
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Annual Research Report
  • [Presentation] 自己重力粘性ガスの時間大域的な運動について

    • Author(s)
      梅原守道
    • Organizer
      第3回 弘前非線形方程式研究会
    • Place of Presentation
      弘前大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] On a spherically symmetric motion of a self-gravitating viscous gas

    • Author(s)
      Morimichi Umehara
    • Organizer
      Parabolic and Navier-Stokes Equations 2012
    • Place of Presentation
      Palac Bedlewo, Bedlewo, Poland
    • Related Report
      2012 Research-status Report
  • [Remarks] 個人Web ページ

    • URL

      http://www.cc.miyazaki-u.ac.jp/umehara/index.html

    • Related Report
      2013 Final Research Report
  • [Remarks] 宮崎大学研究者総覧

    • URL

      https://srhumdb.miyazaki-u.ac.jp/webopen/search?method=view&id=100000948

    • Related Report
      2013 Annual Research Report
  • [Remarks] 宮崎大学研究者総覧

    • URL

      https://umdb.of.miyazaki-u.ac.jp/webopen/search?method=view&id=100000948

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://info.ibaraki.ac.jp/Profiles/18/0001720/profile.html

    • Related Report
      2011 Research-status Report

URL: 

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

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