Global Large Solutions to the Cauchy Problem of Planar Magnetohydrodynamics Equations with Temperature-Dependent Coefficients

In this paper, we consider planar magnetohydrodynamics (MHD) system when the viscous coefficients and heat conductivity depend on specific volume v and temperature 𝜃 . For technical reasons, the viscous coefficients and heat conductivity are assumed to be proportional to h ( v ) 𝜃 α where h ( v ) is a non-degenerate smooth function satisfying some additional conditions. We prove the existence and uniqueness of the global-in-time classical solution to the Cauchy problem with general large initial data when | α | is sufficiently small and the coefficient of magnetic diffusion ν is suitably large. Moreover, it is shown that the global solution is asymptotically stable as time tends to infinity.