A remark on regularity criterion for the dissipative quasi-geostrophic equations

This paper concerns with a regularity criterion of solutions to the 2D dissipative quasi-geostrophic equations. Based on a logarithmic Sobolev inequality in Besov spaces, the absence of singularities of θ in [0,T ] is derived for θ a solution on the interval [0,T ) satisfying the condition ∇⊥θ ∈ Lr 0,T ;B˙0 p,∞ for 2 p + α r = α, 4 α p ∞. This is an extension of earlier regularity results in the Serrin’s type space Lr (0,T ;Lp). © 2006 Elsevier Inc. All rights reserved.