Global existence and large time behavior of strong solutions to the nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum

We investigate an initial boundary value problem of two-dimensional nonhomogeneous heat conducting magnetohydrodynamic equations. We prove that there exists a unique global strong solution. Moreover, we also obtain the large time decay rates of the solution. Note that the initial data can be arbitrarily large and the initial density allows vacuum states. Our method relies upon the delicate energy estimates and Desjardins’ interpolation inequality (B. Desjardins, Regularity results for two-dimensional flows of multiphase viscous fluids, Arch. Rational Mech. Anal. 137(2) (1997) 135–158).