Abstract
We study the behavior at infinity in time of any global solution theta is an element of C(R+, (H) over dot(2-2 alpha) (R-2)) of the surface quasigeostrophic equation with subcritical exponent 2/3 <= alpha <= 1. We prove that lim(t ->infinity)parallel to theta(t)parallel to(H) (over dot2-2 alpha) = 0. Moreover, we prove also the nonhomogeneous version of the previous result, and we prove that if theta is an element of C(R+, (H) over dot(2-2 alpha) (R-2)) is a global solution, then lim(t ->infinity)parallel to theta(t)parallel to((H) over dot2-2 alpha) = 0.