A Note on Asymptotic Stability of Rarefaction Wave of the Impermeable Problem for Radiative Euler Flows

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 slip boundary condition on an impermeable wall. Different from our recent paper named “Asymptotic stability of rarefaction wave with slip boundary condition for radiative Euler flow”, in this paper we study the initial-boundary value problem with the Neumann boundary condition instead of the Dirichlet boundary on the temperature. Based on the Neumann boundary condition on the temperature, we obtain that the pressure also satisfies the Neumann boundary condition. This observation allows us to establish the local existence and a priori estimates more easily than the case of the Dirichlet boundary condition which is studied in the mentioned paper. Since for the impermeable problem, there are quite a few results available for the Navier-Stokes equations and the radiative Euler equations, it will contribute a lot 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. © 2023, Global Science Press. All rights reserved.