TY - JOUR
T1 - A Note on Asymptotic Stability of Rarefaction Wave of the Impermeable Problem for Radiative Euler Flows
AU - Fan , Lili
AU - Ruan , Lizhi
AU - Xiang , Wei
JO - Communications in Mathematical Analysis and Applications
VL - 4
SP - 357
EP - 387
PY - 2023
DA - 2023/11
SN - 2
DO - http://doi.org/10.4208/cmaa.2023-0006
UR - https://global-sci.org/intro/article_detail/cmaa/22147.html
KW - Radiative Euler equations, slip boundary condition, asymptotic stability,
rarefaction wave.
AB - <p style="text-align: justify;">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.</p>