The combined non-equilibrium diffusion and low Mach number limits of a model arising in radiation magnetohydrodynamics

Abstract

We consider the combined non-equilibrium diffusion and low Mach limits of a model arising in radiation magnetohydrodynamics, which is described by the ideal compressible magnetohydrodynamic equations coupled to the radiation transfer equation. We study the case that the temperature has a large variation. In this situation, due to the complex asymmetric singular structure in the model, it is very hard to obtain uniform estimates of solutions in standard Sobolev spaces. To overcome the difficulties caused by the singular structure, we introduce two new weighted norms and construct new auxiliary equations. In the appropriate normed spaces, we show that the contribution of singular terms to the total energy is bounded by O(ϵ) with respect to the parameter ϵ, and then establish the uniform estimates of solutions. Moreover, we rigorously prove that, for the well-prepared initial data, the target system is a coupling of the nonhomogeneous incompressible magnetohydrodynamic equations and a diffusion equation.