On the stability of global solutions to the 3D Boussinesq system

In this paper, we investigate the stability to any given global smooth solutions of the 3D Boussinesq system. Assuming that (θ¯,u¯) is a global solution (called reference solution later) with initial data (θ¯0,u¯0), we prove that a small perturbation of (θ¯0,u¯0) still generates a global smooth solution to the Boussinesq system, and this solution keeps close to the reference solution.