Boundary-layer effects for the 2-D Boussinesq equations with vanishing diffusivity limit in the half plane

The main purpose of this paper is to justify the Stokes–Blasius law of boundary-layer thickness for the 2-D Boussinesq equations with vanishing diffusivity limit in the half plane, i.e., we shall prove that the boundary-layer thickness is of the value δ(ε)=εα with any α (0,1/2) for small diffusivity coefficient ε>0. Moreover, the convergence rates of the vanishing diffusivity limit are also obtained.