Global Regularity for a Modified Critical Dissipative Quasi-geostrophic Equation

In this paper, we consider the modified quasi-geostrophic equation partial derivative(t)theta + (u . del)theta + kappa Lambda(alpha theta) = 0 u = Lambda R-alpha-1(perpendicular to)theta, with kappa > 0, alpha is an element of (0,1] and theta(0) is an element of L-2(R-2). We remark that the extra Lambda(alpha-1) is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regularity of strong solutions to this system.