## The Annals of Probability

### Invariant measure for the stochastic Navier–Stokes equations in unbounded 2D domains

#### Abstract

Building upon a recent work by two of the authors and J. Seidler on $bw$-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an invariant measure to stochastic 2-D Navier–Stokes (with multiplicative noise) equations in unbounded domains. This answers an open question left after the first author and Y. Li proved a corresponding result in the case of an additive noise.

#### Article information

Source
Ann. Probab., Volume 45, Number 5 (2017), 3145-3201.

Dates
Revised: June 2016
First available in Project Euclid: 23 September 2017

https://projecteuclid.org/euclid.aop/1506132035

Digital Object Identifier
doi:10.1214/16-AOP1133

Mathematical Reviews number (MathSciNet)
MR3706740

Zentralblatt MATH identifier
06812202

#### Citation

Brzeźniak, Zdzisław; Motyl, Elżbieta; Ondrejat, Martin. Invariant measure for the stochastic Navier–Stokes equations in unbounded 2D domains. Ann. Probab. 45 (2017), no. 5, 3145--3201. doi:10.1214/16-AOP1133. https://projecteuclid.org/euclid.aop/1506132035

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