Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection
Texas State University, Department of Mathematics
This article concerns the initial-boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with ill-prepared initial data. We consider a non-slip boundary condition for the velocity field and inhomogeneous Dirichlet boundary condition for the temperature. By means of multi-scale analysis and matched asymptotic expansion methods, we establish an accurate approximating solution for the viscous and diffusive Boussinesq system. We also study the convergence of the infinite Prandtl number limit.
Boussinesq system, Rayleigh-Benard convection, Infinite Prandtl number limit, Initial-boundary layer, Asymptotic expansion
Fan, X., Wang, S., Xu, W. Q. (2020). Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection. <i>Electronic Journal of Differential Equations, 2020</i>(31), pp. 1-20.