On the 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 global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces $L^p,$ \mbox{with $p\in [1,\infty ].$ Local results for arbitrary initial data are also given.