Regularity Criteria for the Dissipative Quasi-geostrophic Equations in Hölder Spaces

We study regularity criteria for weak solutions of the dissipative quasi-geostrophic equation (with dissipation (−∆)γ/2, 0 < γ ≤ 1). We show in this paper that if θ ∈ C((0, T ); C1−γ), or θ ∈ Lr((0, T ); Cα) with α = 1−γ+ γ r is a weak solution of the 2D quasi-geostrophic equation, then θ is a classical solution in (0, T ]× R2. This result improves our previous result in [18].