Unique Measure for the Time-Periodic Navier-Stokes on the Sphere

Abstract

This paper proves the existence and uniqueness of a time-invariant measure for the 2D Navier-Stokes equations on the sphere under a random kick-force and a time-periodic deterministic force. Several examples of deterministic forces satisfying the necessary conditions for there to be a unique invariant measure are given. The support of the measure is examined and given explicitly for several cases.