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On asymptotic stability of the 3D Boussinesq equations without heat conduction

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Abstract

We investigate the asymptotic stability of the solutions to Boussinesq equations without heat conduction with the initial data near a specific stationary solution in the three-dimensional domain \(\Omega = {\mathbb{R}^2} \times (0,1)\). It is shown that the solution starting from a small perturbation to the stationary solution converges to it with explicit algebraic rates as time tends to infinity.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 12071211). The authors take this opportunity to thank the referees for their helpful comments.

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Authors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing, 211816, China

    Lihua Dong

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Yongzhong Sun

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  1. Lihua Dong
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  2. Yongzhong Sun
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Correspondence to Yongzhong Sun.

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Dong, L., Sun, Y. On asymptotic stability of the 3D Boussinesq equations without heat conduction. Sci. China Math. 67, 253–280 (2024). https://doi.org/10.1007/s11425-022-2101-9

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  • DOI: https://doi.org/10.1007/s11425-022-2101-9

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