非等熵气体动力学方程组大初值问题的放缩框架

A Scaling Framework for the Non-isentropic Gas Dynamics System with Large Initial Data

非等熵气体动力学系统Cauchy问题弱解全局存在性有两个公开问题:一个是包含真空的小初值问题,另一个是任意大初值问题.本文通过引入一个放缩框架证明了上述两个问题的等价性,即对于粘性消失解,其包含真空小初值问题的一致BV估计蕴含着任意大初值问题弱解的全局存在性.该放缩框架对大多数具有物理背景的双曲守恒律系统亦成立.

There are two open problems on the global existence results of non-isentropic gas dynamics.One is whether the weak solutions exist globally with small initial data containing vacuum,the other is whether the global existence results hold with arbitrary large initial data.By introducing a scaling framework,we give the equivalence of the two problems above.For vanishing viscosity solutions,the positive answer to the first question naturally implies the positive answer to the second one.And this scaling framework can be applied to most systems of conservation laws with physical background.