Global solutions to planar magnetohydrodynamic equations with radiation and large initial data

Abstract

The existence and uniqueness of the global classical solution for the planar magnetohydrodynamic equations are proved for large initial data. The model equations are coupled with the thermal radiation and are supplemented with free boundary and initial conditions. The existence proof relies on the classical Leray–Schauder fixed theorem together with some new a priori estimates in Lagrangian coordinates. The result holds for more general heat conductivity, which is plausible and interesting in physics. Particularly, it is also valid for the case of constant transport coefficients.