ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION*

doi:10.1007/s10473-023-0306-1

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (3): 1081-1104.doi: 10.1007/s10473-023-0306-1

ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*

Xueke Pu, Wenli Zhou^†

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

收稿日期:2021-09-18 修回日期:2022-10-17 出版日期:2023-06-25 发布日期:2023-06-06
通讯作者: ^† Wenli Zhou, E-mail: wywlzhou@163.com
作者简介:Xueke Pu, E-mail: puxueke@gmail.com
基金资助:
Pu was supported in part by the NNSF of China (11871172) and the Science and Technology Projects in Guangzhou (202201020132). Zhou was supported by the Innovation Research for the Postgraduates of Guangzhou University (2021GDJC-D09).

ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*

Xueke Pu, Wenli Zhou^†

School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China

Received:2021-09-18 Revised:2022-10-17 Online:2023-06-25 Published:2023-06-06
Contact: ^† Wenli Zhou, E-mail: wywlzhou@163.com
About author:Xueke Pu, E-mail: puxueke@gmail.com
Supported by:
Pu was supported in part by the NNSF of China (11871172) and the Science and Technology Projects in Guangzhou (202201020132). Zhou was supported by the Innovation Research for the Postgraduates of Guangzhou University (2021GDJC-D09).

摘要/Abstract

摘要： In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.

关键词: Boussinesq equations, primitive equations, density stratification, hydrostatic approximation, strong convergence

Abstract: In this paper, we rigorously derive the governing equations describing the motion of a stable stratified fluid, from the mathematical point of view. In particular, we prove that the scaled Boussinesq equations strongly converge to the viscous primitive equations with density stratification as the aspect ratio goes to zero, and the rate of convergence is of the same order as the aspect ratio. Moreover, in order to obtain this convergence result, we also establish the global well-posedness of strong solutions to the viscous primitive equations with density stratification.

Key words: Boussinesq equations, primitive equations, density stratification, hydrostatic approximation, strong convergence

Xueke Pu, Wenli Zhou. ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*[J]. 数学物理学报(英文版), 2023, 43(3): 1081-1104.

Xueke Pu, Wenli Zhou. ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*[J]. Acta mathematica scientia,Series B, 2023, 43(3): 1081-1104.

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ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*

ON THE RIGOROUS MATHEMATICAL DERIVATION FOR THE VISCOUS PRIMITIVE EQUATIONS WITH DENSITY STRATIFICATION^*

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