Existence and regularity of invariant measures for the three dimensional stochastic primitive equations

Nathan Glatt-Holtz; Igor Kukavica; Vlad Vicol; Mohammed Ziane

doi:10.1063/1.4875104

Existence and regularity of invariant measures for the three dimensional stochastic primitive equations

Nathan Glatt-Holtz, Igor Kukavica, Vlad Vicol, Mohammed Ziane

Mathematics

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46 Scopus citations

Abstract

We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions and is furthermore shown to have higher regularity properties.

Original language	English (US)
Article number	051504
Journal	Journal of Mathematical Physics
Volume	55
Issue number	5
DOIs	https://doi.org/10.1063/1.4875104
State	Published - May 28 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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abstract = "We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions and is furthermore shown to have higher regularity properties.",

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AU - Vicol, Vlad

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N2 - We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions and is furthermore shown to have higher regularity properties.

AB - We establish the continuity of the Markovian semigroup associated with strong solutions of the stochastic 3D Primitive Equations, and prove the existence of an invariant measure. The proof is based on new moment bounds for strong solutions. The invariant measure is supported on strong solutions and is furthermore shown to have higher regularity properties.

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Existence and regularity of invariant measures for the three dimensional stochastic primitive equations

Abstract

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