Stochastically perturbed Navier-Stokes system on the rotating sphere

Abstract

We show the existence and uniqueness of an invariant measure for the kick-forced Navier-Stokes system on the 2-dimensional sphere, first without deterministic force and then with a time-independent deterministic force. The existence and uniqueness of an invariant measure for the white noise forced Navier-Stokes system on the 2-dimensional sphere without a deterministic forcing is also shown. We examine the support of the invariant measure and give a description of the support of the measure in general, and in several special cases, for the kick-forced flow. The support of the invariant measure for the white noise forced equations is shown to be the entire space of admissible vector fields of the sphere.