粘性依赖密度的Navier-Stokes方程组的不连续解

Discontinuous Solutions of the Navier-Stokes Equations for Compressible Flow with Density-Dependent Viscosity

该文研究了一类粘性系数依赖于密度的一维可压缩Navier-Stokes方程组的自由边界问题.对初始密度是不连续的情形,证明了其解的局部存在性和唯一性.其结果说明:不论初始密度的振荡幅度有多大,在某个时间段[0,T]上,气体内部不会产生真空状态,气体和真空的分界也是以有限速度传播的.

In this paper, the author studies the free boundary problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity. The author proves the local （in time） existence and uniqueness result with discontinuous initial density. The important physical consequences of the result are that no vacuum states can occur in the interior of the gas, and the interface separating the gas and vacuum propagates with finite speed in local time, no matter how large the oscillation of the initial density.