Global well-posedness and blow-up criterion for the periodic quasi-geostrophic equations in Lei-Lin-Gevrey spaces

In this paper we consider a periodic 2-dimensional quasi-geostrophic equations with subcritical dissipation. We show the global existence and uniqueness of the solution theta is an element of C ([0, T], gamma(1-2 alpha)(a,sigma)(T-2)) for small initial data in the Lei-Lin-Gevrey spaces. gamma(1-2 alpha)(a,sigma)(T-2). Moreover, we establish an exponential type explosion in finite time of this solution.