Global strong solutions to planar radiative magnetohydrodynamic equations with density-dependent viscosity and degenerate heat-conductivity

Abstract

In this paper, we consider the initial-boundary-value problem for planar magnetohydrodynamics equations. In particular, the influence of radiation on the dynamics at high-temperature regimes is taken into account. For the viscosity depending on the specific volume of the gas and the heat-conductivity proportional to a positive power of the temperature, we establish the global existence and uniqueness of strong solutions with large initial data to the initial-boundary-value problem, which means no shock wave, vacuum, or mass or heat concentration will be developed in finite time, although the interaction between the magnetodynamic effects and hydrodynamic is complex and the motion of the flow has large oscillations.