广义Chaplygin气体下等熵可压缩欧拉方程奇点的形成

Singularity Formation for Isentropic Compressible Euler Equations with Generalized Chaplygin Gas

本文主要研究广义Chaplygin气体在等熵可压缩欧拉方程下奇点的形成问题。首先通过相关方程和准备知识,做一些变量的特征分解,以此来建立梯度变量和黎卡提方程;最后通过给出密度的下界估计来分析奇点的形成。

In this paper, we consider singularity formation for isentropic compressible Euler equations with generalized Chaplygin gas. Firstly, through the relative equations and preliminaries, we do the characteristic decompositions of some variables, in order to establish the gradient variables and Riccati equations. Finally, we analyze the formation of singularity by giving the lower bound estimation of density.