Existence and stability of steady-state solutions to the quasi-geostrophic equations in ℝ2

Abstract

We consider the stationary quasi-geostrophic equation in the whole space driven by a force f. Under certain smallness assumptions of f, we establish the existence of solutions with finite L2 norm. This solution is unique among all solutions with finite energy. The unique solution is also shown to be stable in the sense: any solution of the evolutionary quasi-geostrophic equation driven by f and starting with finite energy, will return to .