Abstract
This paper establishes the global stability for the 2D Boussinesq system with partial dissipation and horizontal thermal diffusion. When there is no thermal diffusion, the stability of the temperature gradient remains an open problem. We extend the \(H^1\)-stability in [7] to \(H^2\)-stability which we care about and obtain the large time behavior of the linearized system.
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Acknowledgements
Wei is supported by the National Key R&D Program of China (2017YFC0601505); National Natural Science Foundation for General Program of China (41672325); Opening Fund of Geomathematics Key Laboratory of Sichuan Province (scsxdz2019zd03) and Li is supported by the Science and Technology Department of Sichuan Province (No. 2017JY0205).
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Wei, Y., Li, D. Stability of the 2D Boussinesq System with Partial Dissipation. J Dyn Diff Equat 33, 1615–1624 (2021). https://doi.org/10.1007/s10884-020-09870-3
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DOI: https://doi.org/10.1007/s10884-020-09870-3