Global well-posedness of the 2D critical dissipative quasi-geostrophic equation in the Triebel–Lizorkin spaces

We prove global well-posedness of the 2D critical dissipative quasi-geostrophic equation for small initial data in the Triebel–Lizorkin spaces Fp,qs,s>2p,p,q∈(1,∞). In particular, our result implies the global existence for small initial data in the Sobolev space Hs,p,s>2p,p∈(1,∞) since Fp,2s=Hs,p. The key ingredients of our proof are the pointwise exponential decay estimate of the semigroup e−tκ(−Δ)α and maximum principle.