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# Regularity of H\"older continuous solutions of the supercritical quasi-geostrophic equation

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### Abstract

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 H\"{o}lder 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 $$(t_0,t]$$.

### Author and article information

###### Journal
21 January 2007
###### Article
10.1016/j.anihpc.2007.10.001
math/0701592
76D03, 35Q35
math.AP