The Annals of Probability

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

Zdzisław Brzeźniak, Elżbieta Motyl, and Martin Ondrejat

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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

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

Received: February 2015
Revised: June 2016
First available in Project Euclid: 23 September 2017

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60] 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 37L40: Invariant measures
Secondary: 76M35: Stochastic analysis 60J25: Continuous-time Markov processes on general state spaces

Invariant measure $bw$-Feller semigroup stochastic Navier–Stokes equations


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.

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