Mathematical analysis of the continuum model of astronomical objects

本文从可压缩粘性流体的基本方程出发，采用连续介质近似对天体进行了数学建模，并通过数学分析验证了建模的合理性。我们得到了以下两个主要结果：（1）在理想气体模型和气体运动都是一维的情况下，我们证明了气体的运动长期稳定存在，而不考虑初始数据的大小。(2)在气体运动是空间三维球对称的情况下，我们证明了气体运动的长时间稳定性与情形（1）相同。

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).