On regularity criterion for the dissipative quasi-geostrophic equations

In this paper we consider the 2D dissipative quasi-geostrophic equations and study the regularity criterion of the solutions. By means of a commutator estimate based on frequency localization and Bony’s paraproduct decomposition, we obtain a regularity criterion ∇⊥θ ∈ Lr 0,T ;B˙0 p,∞ for 2 p + α r α, 2 α p ∞, which is an obvious extension of the result in [B. Dong, Z. Chen, A remark on regularity criterion for the dissipative quasigeostrophic equations, J. Math. Anal. Appl. 329 (2007) 1212–1217] where their restrictive condition on p is 4 α p ∞. © 2007 Elsevier Inc. All rights reserved.