Asymptotic stability of rarefaction wave with non-slip boundary condition for radiative Euler flows

Abstract

This paper is devoted to studying the initial-boundary value problem for the radiative full Euler equations, which are a fundamental system in the radiative hydrodynamics with many practical applications in astrophysical and nuclear phenomena, with the non-slip boundary condition on an impermeable wall. Due to the difficulty from the disappearance of the velocity on the impermeable boundary, quite few results for compressible Navier-Stokes equations and no result for the radiative Euler equations are available at this moment. So the asymptotic stability of the rarefaction wave proven in this paper is the first rigorous result on the global stability of solutions of the radiative Euler equations with the non-slip boundary condition. It also contributes to our systematical study on the asymptotic behaviors of the rarefaction wave with the radiative effect and different boundary conditions such as the inflow/outflow problem and the impermeable boundary problem in our series papers including [5], [6].