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.
|School:||University of Missouri - Columbia|
|School Location:||United States -- Missouri|
|Source:||DAI-B 75/03(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Invariant measure, Kick-forced flow, Perturbed Navier-Stokes system, Rotating sphere|
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