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Long-Time Behavior of Global Solutions of Anisotropic Quasi-Geostrophic Equations in Sobolev Space

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Abstract

In this study, we investigate the long-time behavior of the global solution of the anisotropic quasi-geostrophic equation, denoted by \(\theta \), where \(\theta \) belongs to the space \(C_b({\mathbb {R}}^+,H^s({\mathbb {R}}^2))\). Our results demonstrate that the solution decays to zero as time approaches infinity in the \(L^p({\mathbb {R}}^2)\) norm, with \(p\ge 2\). Additionally, we establish that the limit of \(\Vert \theta (t)\Vert _{H^s}\) approaches zero as t tends to infinity.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science of Gabès, Research Laboratory Mathematics and Applications LR17ES11, Gabès, Tunisia

    Mustapha Amara

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  1. Mustapha Amara
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Correspondence to Mustapha Amara.

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Communicated by Maria Alessandra Ragusa.

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Amara, M. Long-Time Behavior of Global Solutions of Anisotropic Quasi-Geostrophic Equations in Sobolev Space. Bull. Malays. Math. Sci. Soc. 46, 166 (2023). https://doi.org/10.1007/s40840-023-01564-5

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