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

Gregory Varner^*

Division of Natural and Health Sciences, Mathematics Department, John Brown University, Siloam Springs, USA.

DOI: 10.4236/am.2015.611160                

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 force satisfying the necessary conditions for a unique invariant measure to exist are given. The support of the measure is examined and given explicitly for several cases.

Keywords

Navier-Stokes, Invariant Measure, Sphere

Conflicts of Interest

The authors declare no conflicts of interest.

References

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