Electron. J. Differential Equations, Vol. 2022 (2022), No. 33, pp. 1-18.

Initial layer associated with Boussinesq systems for thermosolutal convection

Xiaoting Fan, Wei Wang

Abstract:
This article concerns the behavior of the initial layer appearing at large Prandtl number in Boussinesq equations with the ill initial data. By using the asymptotic expansion methods of singular perturbation theory, we establish an approximate solution and the rate of convergence as the Prandtl number tends to infinity. Our results improve the existing ones concerning thermosolutal convection.

Submitted November 16, 2021. Published April 21, 2022.
Math Subject Classifications: 35Q35, 35B20, 35C20.
Key Words: Boussinesq system; thermosolutal convection; Prandtl number; perturbation theory; asymptotic expansion. DOI: https://doi.org/10.58997/ejde.2022.33

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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
Wei Wang
College of Mathematics and Systems Science
Shandong University of Science and Technology
Qingdao 266590, China
email: weiw10437@163.com

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