Global Strong Solution to the Nonhomogeneous Bénard System with Large Initial Data and Vacuum

Abstract

We establish a unique global strong solution for nonhomogeneous Benard system with zero density at infinity on the whole two-dimensional (2D) space. In particular, the initial data can be arbitrarily large and the initial density can contain vacuum states and even have compact support. Our method relies heavily on the structure of the system under consideration and spatial dimension.