  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 $(t_0,t]$.
