Dissipative quasi-geostrophic dynamics under random forcing

The quasi-geostrophic model is a simplified geophysical fluid model at asym ptotically high rotation rate or at small Rossby number. We consider the qu asi-geostrophic equation with dissipation under random forcing in bounded d omains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasi-geostrophic equation whose well-posedn ess is well known, there seems to be no rigorous result on global existence and uniqueness of the randomly forced quasi-geostrophic equation. Our work provides such a rigorous result on global existence and uniqueness, under very mild conditions. (C) 1998 Academic Press.