Global well-posedness to the 3D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large oscillations and vacuum

Abstract

We consider the Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with vacuum in R3. Based on delicate energy estimates, we establish the global existence and uniqueness of strong solutions under some smallness condition. Moreover, we also derive large-time decay rates of the solution. In particular, our smallness condition is independent of any norms of the initial data except the upper bound of the initial density.