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

 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 . Received: 24 April 2002 / Accepted: 29 July 2002 Published online: 10 December 2002 Communicated by P. Constantin