The decay and stability of solutions for the 3D density-dependent incompressible Boussinesq system

This paper deals with stability and the large-time decay to any given global smooth solutions of the 3D density-dependent incompressible Boussinesq system. The decay rate for solutions of the corresponding Cauchy problem is obtained in this work. With the aid of this decay rate, it is shown that a small perturbation of initial data $(overline{a}_0,overline{theta}_0, overline{u}_0)$ still generates a global smooth solution to the density-dependent Boussinesq system, and this solution keeps close to the reference solution.