Vanishing diffusivity limit for the 3D heat-conductive Boussinesq equations with a slip boundary condition

In this paper, we consider the 3D heat-conductive Boussinesq equations with a slip boundary condition for the velocity field and Neumann boundary condition for the temperature. We prove that there exists an interval of time which is uniform for the heat conductivity coefficient κ and for which the 3D heat-conductive Boussinesq equations have a strong solution. The solution is uniformly bounded in some spaces with respect to κ. Based on these uniform estimates, we establish the vanishing diffusivity limit for the Boussinesq equations and also obtain the convergence rates for the velocity field and the temperature.