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

TL;DR

This paper establishes the existence and uniqueness of a time-invariant measure for the 2D Navier-Stokes equations on the sphere with combined random and periodic deterministic forcing, analyzing its support explicitly.

Contribution

It introduces a novel approach to proving uniqueness of invariant measures for Navier-Stokes on the sphere with time-periodic forces and characterizes the measure's support.

Findings

Existence of a unique invariant measure under specified conditions

Explicit characterization of the measure's support in several cases

Examples of deterministic forces satisfying the conditions

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.