Asymptotic Stability of Shock Wave for the Outflow Problem Governed by the One-Dimensional Radiative Euler Equations

Abstract

This paper is devoted to the study of the asymptotic stability of the shock wave of the outflow problem governed by the one-dimensional radiative Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena. The outflow problem means that the flow velocity on the boundary is negative. Comparing with our previous work on the asymptotic stability of the rarefaction wave of the outflow problem for the radiative Euler equations in [6], two points should be pointed out. On one hand, boundary condition on velocity is considered instead of boundary condition on temperature, which induces a perfect boundary condition on anti-derivative perturbations so that boundary estimates on perturbed unknowns are trickily and smoothly established. On the other hand, the rarefaction wave is an expansive wave, while the shock wave is a compressive wave. So we need take good advantages of properties of the shock wave instead. Our investigation on the outflow problem provides a good understanding on the radiative effect and boundary effect in the setting of shock wave.