Global Well-Posedness in the Super-Critical Dissipative Quasi-Geostrophic Equations

Abstract

We consider the quasi-geostrophic equation with the dissipation term, κ (-Δ)α θ, \(\) In the case \(\), Constantin-Cordoba-Wu [6] proved the global existence of strong solution in H 1 and H 2 under the assumption of small L ∞ -norm of initial data. In this paper, we prove the global existence in the scale invariant Besov space, B 2−2α 2,1 , \(\) for initial data small in the B 2−2α 2,1 norm. We also prove a global stability result in B 1 2,1 .