Vanishing Viscosity Limit For The 3D Boussinesq Equations With Slip Boundary Conditions

In this paper, we study vanishing viscosity limits of the 3-dimensional in-compressible Boussinesq system in smooth bounded domains with slip boundary.Here we show the well-posedness to the initial boundary value problem for such system, under the condition of the initial vorticity to be zero, it can prove an extra boundary condition that the vorticity of the ideal Boussinesq equations keep invariant with the time evolution. Then we obtain the strong convergence of solutions to Boussinesq equations and obtain a convergence result with slip boundary condition.