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Unique Measure for the Time-Periodic Navier-Stokes on the Sphere Navier-Stokes on the Sphere
Division of Natural and Health Sciences, Mathematics Department, John Brown University, Siloam Springs, USA
- 1 Division of Natural and Health Sciences, Mathematics Department, John Brown University, Siloam Springs, USA
Applied Mathematics·Volume 06 (2015)·Pages 1809–1830·Published 16 October 2015·DOI10.4236/am.2015.611160
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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.
KeywordsNavier-StokesInvariant MeasureSphere
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