Electron. J. Differential Equations, Vol. 2020 (2020), No. 31, pp. 1-20.

Initial-boundary layer associated with the 3-D Boussinesq system for Rayleigh-Benard convection

Xiaoting Fan, Shu Wang, Wen-Qing Xu

Abstract:
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.

Submitted October 12, 2019. Published April 7, 2020.
Math Subject Classifications: 35B25, 35B40, 35K57.
Key Words: Boussinesq system; Rayleigh-Benard convection; infinite Prandtl number limit; initial-boundary layer; asymptotic expansion.
DOI: 10.58997/ejde.2020.31

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Xiaoting Fan
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: xiao_ting_fan@163.com
Shu Wang
College of Applied Sciences
Beijing University of Technology
Ping Le Yuan100, Chao Yang District
Beijing 100124, China
email: wangshu@bjut.edu.cn}
Wen-Qing Xu
Department of Mathematics and Statistics
California State University
Long Beach, California 90840, USA
email: wxu@csulb.edu

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