Dissipative Quasi-geostrophic Dynamics under Random Forcing*

The quasi-geostrophic model is a simplified geophysical fluid model at asymptotically high rotation rate or at small Rossby number. We consider the quasi-geostrophic equation with dissipation under random forcing in bounded domains. We show that global unique solutions exist for appropriate initial data. Unlike the deterministic quasi-geostrophic equation whose well-posedness 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.