Global Well-Posedness and Exponential Decay of Strong Solution to the Three-Dimensional Nonhomogeneous Bénard System with Density-Dependent Viscosity and Vacuum

In this paper, we are concerned with the three-dimensional nonhomogeneous Bénard system with density-dependent viscosity in bounded domain. The global well-posedness of strong solution is established, provided that the initial total mass ${\parallel {\rho }_0\parallel }_{L^1}$ $\|\rho _{0}\|_{L^{1}}$ is suitably small. In particular, the initial velocity and temperature can be arbitrarily large. Moreover, the exponential decay of strong solution is also obtained. It is worth noting that the vacuum of initial density is allowed.