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arXiv · 2112.10164

Global solution of anisotropic Quasi-Geostrophic Equations in Sobolev Space

Mustapha Amara·Jamel Benameur
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Abstract

In \cite{YZ}, the author proved the global existence of the two-dimensional anisotropic quasi-geostrophic equations with condition on the parameters $\alpha,$ $\beta$ in the Sobolev spaces $H^s( \R^2)$; $s\geq 2$. In this paper, we show that this equations has a global solution in the spaces $H^s(\R^2)$, where $\max\{2-2\alpha,2-2\beta\}< s<2$, with additional condition over $\alpha$ and $\beta$. The proof is based on the Gevrey-class regularity of the solution in neighborhood of zero.

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Mustapha Amara, Jamel Benameur. 2021-12-19. Global solution of anisotropic Quasi-Geostrophic Equations in Sobolev Space. https://arxiv.org/abs/2112.10164

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