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On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification

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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.

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Authors and Affiliations

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

    Xueke Pu  (蒲学科) & Wenli Zhou  (周文利)

Authors
  1. Xueke Pu  (蒲学科)
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  2. Wenli Zhou  (周文利)
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Corresponding author

Correspondence to Wenli Zhou  (周文利).

Additional information

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).

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Pu, X., Zhou, W. On the Rigorous Mathematical Derivation for the Viscous Primitive Equations with Density Stratification. Acta Math Sci 43, 1081–1104 (2023). https://doi.org/10.1007/s10473-023-0306-1

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  • DOI: https://doi.org/10.1007/s10473-023-0306-1

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