In this paper we consider the initial boundary value problem for the 3D Boussinesq system with the velocity dissipation and weak damping effect to instead of the dissipation effect for the thermal conductivity and establish the global existence of weak solutions. Furthermore, we prove that the global weak solution is strong and unique under some small initial data condition.
"Initial boundary value problem for 3D Boussinesq system with the thermal damping." Osaka J. Math. 57 (1) 61 - 83, January 2020.