Global well-posedness to the Cauchy problem of 2D inhomogeneous incompressible magnetic Benard equations with large initial data and vacuum

In this paper, we are concerned with the Cauchy problem of inhomogeneous incompressible magnetic Benard equations with vacuum as far-field density in R-2. We prove that if the initial density and magnetic field decay not too slowly at infinity, the system admits a unique global strong solution. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states and even has compact support. Moreover, we extend the result of [16,17] to the global one.