Long time dynamics of 2D quasi-geostrophic equations with damping in

The long time behavior of solutions of 2D quasi-geostrophic equations with damping on the whole space is studied. The existence of the global attractor in L p is proved. New difficulties come from nonlocal terms and the Banach space L p . We overcome them by using commutator estimates and positivity inequalities associated with fractional Laplacian.