Existence and uniqueness results for the 2-D dissipative quasi-geostrophic equation

This paper concerns itself with Besov space solutions of the 2-D quasi-geostrophic (QG) equation with dissipation induced by a fractional Laplacian (-Delta)alpha(.) The goal is threefold: first, to extend a previous result on solutions in the inhomogeneous Besov space B-2,q(r) [J. Wu, Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces, SIAM J. Math. Anal. 36 (2004-2005) 1014-1030] to cover the case when r = 2 - 2a; second, to establish the global existence of solutions in the homogeneous Besov space B(over dot)(p,q)(r) with general indices p and q; and third, to determine the uniqueness of solutions in any one of the four spaces: B-p,q(S), B(over dot)(2,q)(r),L-q((0,T); B-2,q(s+2 alpha/q)) and L-q((0,T); B(over dot)(p,q)(r+2 alpha/q)), where s >= 2-2 alpha and r = 1-2 alpha + 2/p (c) 2006 Elsevier Ltd. All rights reserved.