Boundary layers associated with the 3-D Boussinesq system for Rayleigh–Bénard convection. Issue 12 (9th September 2020) - Fan, Xiaoting; Xu, Wen-Qing; Wang, Shu; Wang, Wei
Abstract : We investigate the boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh–Bénard convection with vanishing diffusivity limit. By adopting the multi-scale analysis and the asymptotic expansion methods of singular perturbation theory, we construct an exact approximating solution for the viscous and diffusive Boussinesq system with well-prepared initial data. In addition, we obtain the convergence result of the vanishing diffusivity limit.