A regularizing effect of radiation in one-dimensional compressible MHD equations

This paper is concerned with the global existence of classical solutions to an initial–boundary value problem of the one-dimensional (1D) equations of compressible radiative magnetohydrodynamics (MHD). The key point here is that there is no growth restriction imposed on the heat conductivity, in particular, the heat-conducting coefficient is allowed to be a positive constant. This in particular implies that the radiation is indeed a mathematically “regularizing” effect on the fluid dynamics, since the global existence of the classical solution to the one-dimensional full perfect MHD equations without radiation is still unknown when all the viscosity, magnetic diffusivity and heat conductivity coefficients are constant.