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

Abstract

This paper establishes the global well-posedness of strong solutions to the nonhomogeneous Bénard system with positive density at infinity in the whole space R2. We obtain the global existence and uniqueness of strong solutions for general large initial data. Our method relies on the dedicate energy estimates and a logarithmic interpolation inequality.