Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces

Abstract

In this paper we study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove a global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces L p , with p ∈ [ 1 , ∞ ] . Local results for arbitrary initial data are also given.