A limit problem for three-dimensional ideal compressible radiation magneto-hydrodynamics

Abstract

General radiation magnetic hydrodynamics models include two main parts that are coupled: one part is the macroscopic magnetic fluid part, which is governed by the ideal compressible magnetohydrodynamic (MHD) equations with additional radiation terms; another part is the radiation field, which is described by a transfer equation. It is well known that in radiation hydrodynamics without a magnetic field there are two physical approximations: one is the so-called P1 approximation and the other is the so-called gray approximation. Starting out with a general radiation MHD model one can derive the so-called MHD-P1 approximation model. In this paper, we study the non-relativistic type limit for this MHD-P1 approximation model since the speed of light is much larger than the speed of the macroscopic fluid. This way we achieve a rigorous derivation of a widely used macroscopic model in radiation magnetohydrodynamics.