### Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity

Röckner M, Zhang X (2009)
Probability Theory and Related Fields 145(1-2): 211-267.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Einrichtung
Abstract / Bemerkung
In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly (Ann. Math. 164:993-1032, 2006), we prove the uniqueness of invariant measures for the corresponding transition semigroup.
Stichworte
Invariant measure; Navier-Stokes equation; Ergodicity; Asymptotic; strong Feller property
Erscheinungsjahr
2009
Zeitschriftentitel
Probability Theory and Related Fields
Band
145
Ausgabe
1-2
Seite(n)
211-267
ISSN
0178-8051
Page URI
https://pub.uni-bielefeld.de/record/1633336

### Zitieren

Röckner M, Zhang X. Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity. Probability Theory and Related Fields. 2009;145(1-2):211-267.
Röckner, M., & Zhang, X. (2009). Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity. Probability Theory and Related Fields, 145(1-2), 211-267. https://doi.org/10.1007/s00440-008-0167-5
Röckner, M., and Zhang, X. (2009). Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity. Probability Theory and Related Fields 145, 211-267.
Röckner, M., & Zhang, X., 2009. Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity. Probability Theory and Related Fields, 145(1-2), p 211-267.
M. Röckner and X. Zhang, “Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity”, Probability Theory and Related Fields, vol. 145, 2009, pp. 211-267.
Röckner, M., Zhang, X.: Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity. Probability Theory and Related Fields. 145, 211-267 (2009).
Röckner, Michael, and Zhang, Xicheng. “Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity”. Probability Theory and Related Fields 145.1-2 (2009): 211-267.

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