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 theta in [0, T] is derived for theta a solution on the interval [0, T) satisfying the condition del(perpendicular to)theta epsilon epsilon L-r (0, T; B-p(0), infinity) for 2/p + alpha/r = alpha, 4/alpha < p <infinity. This is an extension of earlier regularity results in the Serrin's type space L-r (0, T; L-p). (c) 2006 Elsevier Inc. All rights reserved.