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

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

2011-06-10

arxiv.org/abs/1106.2137v2

Mathematics

Analysis of PDEs

11 pages, second version with slightly stronger result

Scientific paper

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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