Global well-posedness to the Cauchy problem of 2D nonhomogeneous magnetic Bénard system with large initial data and vacuum

This paper establishes the global well-posedness of strong solutions to the nonhomogeneous magnetic Bénard system with positive density at infinity in the whole space ${\mathbb{R}}^2$. More precisely, we obtain the global existence and uniqueness of strong solutions for general large initial data. Our method relies on dedicate energy estimates and a logarithmic interpolation inequality.