Global strong solution for compressible and radiative MHD flow with density-dependent viscosity and degenerate heat-conductivity in unbounded domains

Abstract

This paper considers the planar magnetohydrodynamic system with the influence of radiation on the dynamics at high temperature regimes. When the viscosity μ depending on the specific volume of the gas (μ=μ̃1+μ̃2v−α with μ̃1>0,μ̃2≥0) and the heat conductivity κ being a power function of the temperature (κ=κ̃θβ with κ̃>0), the global existence of strong solution with large initial data to the magnetohydrodynamic system is proved in unbounded domains for any α≥0 and β≥0. In particular, the constant coefficients case (μ and κ are positive constants) is also covered in our theorem.