Mathematical analysis of the continuum model of astronomical objects

天体连续介质模型的数学分析

• 批准号: 21840014
• 负责人: UMEHARA Morimichi
• 金额: $ 1.31万
• 依托单位: Ibaraki University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-21840014/
• 关键词: 圧縮性粘性流体; Navier-Stokes方程式; 自由境界問題; 自己重力; 偏微分方程式; 天体の連続体モデル; 解析学; 流体の基礎方程式; 天体物理

We considered the mathematical modelization of astronomical objects by the continuum approximation (based on the basic equation of compressible viscous fluid), and verified the justification of our modeling through mathematical analysis. We obtained the following main two results : (1) On the case that both the model is composed of ideal gas and the gaseous motion is spacially one-dimensional, we proved that the motion of the gas exists for a long time stably without taking the smallness on the size of the initial data. (2) On the case that the gaseous motion is spherically symmetric in spacially three-dimension, we proved the long time stability of the motion of the gas as with the case (1).

我们考虑了连续介质近似（基于可压缩粘性流体的基本方程）对天体的数学建模，并通过数学分析验证了我们建模的合理性。我们主要得到了以下两个结果：（1）在模型均由理想气体组成且气体运动为空间一维的情况下，我们证明了气体的运动长期稳定地存在，而不考虑初始数据规模的小。 (2)在气体运动在空间三维上呈球对称的情况下，与情况(1)一样，我们证明了气体运动的长期稳定性。

项目成果

On the free-boundary problem for self-gravitating viscous gaseous models

自引力粘性气体模型的自由边界问题

• 发表时间: 2009
• 期刊: Seminar Notes of Mathematical Sciences, Ibaraki University Vol.12
• 作者: 大沼久美;武藤潤;長濱裕幸;大槻憲四郎;梅原守道
• 通讯作者: 梅原守道

Global behaviour of the spherically symmetric flow of a self-gravitating viscous gas over the rigid core

自重力粘性气体在刚性核心上球对称流动的全局行为

• 发表时间: 2011
• 作者: Muto;Hirth;Tullis;Heilbronner;梅原守道
• 通讯作者: 梅原守道

Temporally global behaviour of the spherically symmetric flow of a viscous and self-gravitating gas

粘性自引力气体球对称流的时间全局行为

• 发表时间: 2010
• 期刊: International conference on numerical analysis and applied mathematics 2010(edited by T.E.Simos, G. Psihoyios, Ch.Tsitouras)(Amer.Inst.Psys) 1281(AIP Conf.Proc.)
• 作者: 岡崎麻佑;杉本周作;花輪公雄;M.Umehara
• 通讯作者: M.Umehara