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 equation with subcritical dissipation. We show the global existence and uniqueness of the solution mathematical equation for small initial data in the Lei-Lin-Gevrey spaces mathematical equation. Moreover, we establish an exponential-type explosion in finite time of this solution.