Global well-posedness for the 2D critical dissipative quasi-geostrophic equation

We study the initial value problem for the 2D critical dissipative quasi-geostrophic equation. We prove the global existence for small data in the scale invariant Besov spaces Ḃ _p,1 ^2/p , 1 ⩽ p ⩽ ∞. In particular, for p = ∞, our result does not impose any regularity on the initial data. Our proofs are based on an exponential decay estimate of the semigroup and the use of space-time Besov spaces. This work was supported by the National Natural Science Foundation of China (Grant No. 10601002)