Boundary layers associated with the 3-D Boussinesq system for Rayleigh–Bénard convection. Issue 12 (9th September 2020)

• Record Type: Journal Article
• Authors: Fan, Xiaoting; Xu, Wen-Qing; Wang, Shu; Wang, Wei
• Is Part Of: Applicable analysis. Volume 99:Issue 12(2020)
• Page Start: 2026
• Page End: 2044
• Publication Date: 2020-09-09
• Subjects: Ming Mei; Boussinesq system -- Rayleigh–Bénard convection -- vanishing diffusivity limit -- boundary layers -- asymptotic expansion; 35Q35 -- 76W05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1553035
• Languages: English
• ISSNs: 0003-6811

Abstract

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.