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arXiv · 1106.2137

Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

Michael Dabkowski·Alexander Kiselev·Vlad Vicol
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Abstract

We use a nonlocal maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field $u$ is obtained from the active scalar $\theta$ by a Fourier multiplier with symbol $i k^\perp |k|^{-1} m(k|)$, where $m$ is a smooth increasing function that grows slower than $\log \log |k|$ as $|k|\rightarrow \infty$.

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Michael Dabkowski, Alexander Kiselev, Vlad Vicol. 2011-06-10. Global well-posedness for a slightly supercritical surface quasi-geostrophic equation. https://doi.org/10.1088/0951-7715/25/5/1525

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