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][0,T] is derived for θ   a solution on the interval [0,T)[0,T) satisfying the condition∇⊥θ∈Lr(0,T;B˙p,∞0)for2p+αr=α,4α⩽p⩽∞. This is an extension of earlier regularity results in the Serrin's type space Lr(0,T;Lp)Lr(0,T;Lp).