Stability of Basic Wave Patterns for Gas Motions

摘要

AS a typical example of hyperbolic conservation laws, the system of compressible Euler equations representing the conservation of mass, momentum and energy has three basic wave patterns. They are two nonlinear waves called shock and rarefaction wave, and one linearly degenerate wave called contact discontinuity These basic wave patterns have their counterparts both in other physical models for gas motions in equilibrium involving viscosity and heat conductivity, and gas motion in non-equilibrium The stability of these basic wave patterns for the system of compressible Navier-Stokes equations and the Boltzmann equation has been an active research topic and has reached a mature status In this paper, we will give a survey on the stability of these three basic waves patterns for both the compressible Navier-Stokes equations and the Boltzmann equation.