Global Strong Solution and Exponential Decay to the 3D Cauchy Problem of Nonhomogeneous Bénard System with Vacuum

Abstract

We prove the global existence and exponential decay of strong solutions to the Cauchy problem of nonhomogeneous Benard system in $\mathbb{R}^{3}$ provided that some smallness conditions hold true. Note that although the system degenerates near vacuum, there is no need to require compatibility conditions for the initial data via time weighted techniques. The analysis lies on delicate energy estimates and the structure of the system under consideration.