Unique global solution to the thermally radiative magnetohydrodynamics equations

In this paper, we consider a non-equilibrium diffusion approximation model in thermally radiative magnetohydrodynamics (MHD) which describe the compressible viscous, heat-conducting fluid coupled with the Maxwell equations governing the behavior of the magnetic field with taking into account the radiation effect under the non-local thermal equilibrium case. The system consists of the radiative transfer equation coupled with the compressible MHD equations, and the magnetic diffusion coefficient, viscosity coefficient, heat-conducting coefficient are all allowed to be positive constants. We prove existence, uniqueness and regularity of global-in-time classical solutions to one-dimensional case of this model. Based on the fundamental local existence results and global-in-time a priori estimates, we can establish the global existence of a unique classical solutions with large initial data to the initial-boundary value problems.