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
Show me the PDF file (358 KB), TEX file for this article.
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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 |
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Shu Wang College of Applied Sciences Beijing University of Technology Ping Le Yuan100, Chao Yang District Beijing 100124, China email: wangshu@bjut.edu.cn} |
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Wen-Qing Xu Department of Mathematics and Statistics California State University Long Beach, California 90840, USA email: wxu@csulb.edu |
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