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arXiv · 0803.1318

Global regularity for a modified critical dissipative quasi-geostrophic equation

Peter Constantin·Gautam Iyer·Jiahong Wu
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Abstract

In this paper, we consider the modified quasi-geostrophic equation \begin{gather*} \del_t θ+ (u \cdot \grad) θ+ κΛ^αθ= 0 u = Λ^{α- 1} R^{\perp}θ. \end{gather*} with $κ> 0$, $α\in (0,1]$ and $θ_0 \in \lp{2}(\R^2)$. We remark that the extra $Λ^{α- 1}$ is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regularity of strong solutions to this system.

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Peter Constantin, Gautam Iyer, Jiahong Wu. 2008-03-09. Global regularity for a modified critical dissipative quasi-geostrophic equation. https://doi.org/10.1512/iumj.2008.57.3629

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