2010 Fiscal Year Final Research Report

Mathematical analysis of the continuum model of astronomical objects

Research Project

Project/Area Number	21840014
Research Category	Grant-in-Aid for Research Activity Start-up
Allocation Type	Single-year Grants
Research Field	Basic analysis
Research Institution	Ibaraki University
Principal Investigator	UMEHARA Morimichi Ibaraki University, 大学教育センター, 講師 (40532164)
Project Period (FY)	2009 – 2010
Keywords	圧縮性粘性流体 / Navier-Stokes方程式 / 自由境界問題 / 自己重力
Research Abstract	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).