Abstract:

We considered an initialvalue problem for a class of Boussinesq equations using the energy estimate method. We mainly studied the boundary layer effect and the convergence rate as the thermal diffusion parameter ε→0, giving that the boundary layer thickness is of the order O(εβ) with 0<β<2/3. Compared with the existing methods, the present method presented  more thinner BLthickness. In addition, the convergence rate was also improved.

Key words: boundary layer, BL-thickness, convergence rates, vanishing diffusivity limit