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Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation. (English) Zbl 1149.76052
Summary: We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical \((\alpha <1/2)\) dissipation \(( - \Delta )^{\alpha}\): If a Leray-Hopf weak solution is Hölder continuous \(\theta \in C^{\delta }(\mathbb R^2)\) with \(\delta >1 - 2\alpha \) on the time interval \([t_{0},t]\), then it is actually a classical solution on (\(t_{0},t\)].

MSC:
76U05 General theory of rotating fluids
35Q35 PDEs in connection with fluid mechanics
86A10 Meteorology and atmospheric physics
86A05 Hydrology, hydrography, oceanography
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