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Stability near hydrostatic equilibrium to the three-dimensional Boussinesq equations with partial dissipation

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Abstract

This paper focuses on the stability problem for perturbations near a hydrostatic equilibrium associated with the three-dimensional Boussinesq equations with partial dissipation. We mainly study the global stability and large-time behavior of solutions to this system with only horizontal dissipation and obtain three results. The first establishes the global \(H^2\)-stability, the second obtains the large-time asymptotic of the solutions, and the last assesses the asymptotic linear stability with explicit decay rates. Finally, we remark that these results can also be extended to the system with mixed partial dissipation.

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Acknowledgements

The authors would like to thank the anonymous referee for the comments and suggestions, which improve the presentation of the original manuscript.

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  1. School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, Jiaozuo, People’s Republic of China

    Haifeng Shang & Limin Xu

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  1. Haifeng Shang
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  2. Limin Xu
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Correspondence to Haifeng Shang.

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Shang, H., Xu, L. Stability near hydrostatic equilibrium to the three-dimensional Boussinesq equations with partial dissipation. Z. Angew. Math. Phys. 72, 60 (2021). https://doi.org/10.1007/s00033-021-01495-w

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  • DOI: https://doi.org/10.1007/s00033-021-01495-w

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