Abstract
We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−Δ)γ/2, 0 < γ ≤ 1). We show in this paper that if \({\theta \in C((0, T); C^{1-\gamma})}\) , or \({\theta \in L^{r}((0, T); C^\alpha)}\) with \({\alpha = 1 - \gamma + \frac{\gamma}{r}}\) is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in \({(0, T] \times {\mathbb R}^2}\) . This result improves our previous result in [18].
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Communicated by P. Constantin
Partially supported by a start-up funding from the Division of Applied Mathematics of Brown University and NSF grant number DMS 0800129.
Partially supported by a start-up funding from the College of Natural Sciences of the University of Texas at Austin, NSF grant number DMS 0758247 and an Alfred P. Sloan Research Fellowship.
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Dong, H., Pavlović, N. Regularity Criteria for the Dissipative Quasi-Geostrophic Equations in Hölder Spaces. Commun. Math. Phys. 290, 801–812 (2009). https://doi.org/10.1007/s00220-009-0756-x
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DOI: https://doi.org/10.1007/s00220-009-0756-x