Stability of the Damped Three-Dimensional Incompressible Boussinesq Equations

In this paper, we investigate the global well-posedness on the three-dimensional (3D) Boussinesq equation, where the velocity equation and temperature equation involve damping terms, respectively. Without temperature, the corresponding velocity equations is governed by a 3D incompressible anisotropic Navier-Stokes equation, and the stability is still unknown. However, when the velocity fluid is coupled temperature. We first establish the global well-posedness of the Boussinesq equations in H3(R3). Additionally, we alsoobtain the explicit decay rates for the system.