Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit

Xiaoting Fan, Shu Wang, Wen-Qing Xu, Mingshuo Liu
2018 Open Mathematics  
The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates $O(\varepsilon^{\frac{3}{2}})$ and O(ε2).
doi:10.1515/math-2018-0094 fatcat:t5gzivvzdvh2pnwdpvemoytw34