Global well-posedness to the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic equations with large initial data and vacuum

We establish global well-posedness of strong solutions to the nonhomogeneous heat conducting magnetohydrodynamic equations with non-negative density on the whole space R2. More precisely, under compatibility conditions for the initial data, we show the global existence and uniqueness of strong solutions. Our method relies on delicate energy estimates and a logarithmic interpolation inequality. In particular, the initial data can be arbitrarily large.