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

doi:10.1007/s10473-023-0306-1

Abstract

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].Acta mathematica scientia,Series B, 2023, 43(3): 1081-1104.

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References

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

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