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

Abstract

We establish global well-posedness of strong solutions to the nonhomogeneous heat conducting magnetohydrodynamic equations with non-negative density on the whole space $${\mathbb {R}}^2$$ . 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.