Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

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 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 $(t_0,t]$.

References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation

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