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On the Stability of Weak Solution for Compressible Primitive Equations

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Abstract

In this paper, we study a compressible Primitive Equations (CPEs) of the ocean in the two dimensional space, with horizontal periodic and vertical mixed boundary conditions. Thanks to an effective change of variables, we obtain a new CPEs model, which is similar as viscous shallow water equation. Using a new entropy estimate, we prove the stability of weak solutions for this new two dimensional CPEs model.

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Acknowledgements

The authors would like to express their thanks to the editor and referee for their valuable comments. This work is partially supported by China NSF Grant 11171158 and 11271192, National Basic Research Program of China (973 Program) No. 2013CB834100, PAPD of Jiangsu Higher Education Institutions and the Jiangsu Collaborative Innovation Center for Climate Change, the Fundamental Research Funds for the Central Universities 2014B13914.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Hohai University, Nanjing, 210098, P.R. China

    Tong Tang

  2. Jiangsu Key Laboratory for NSLSCS and School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Hongjun Gao

  3. Institute of Mathematics, Jilin University, Changchun, 130012, China

    Hongjun Gao

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  1. Tong Tang
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  2. Hongjun Gao
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Correspondence to Hongjun Gao.

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Tang, T., Gao, H. On the Stability of Weak Solution for Compressible Primitive Equations. Acta Appl Math 140, 133–145 (2015). https://doi.org/10.1007/s10440-014-9982-0

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  • DOI: https://doi.org/10.1007/s10440-014-9982-0

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