The Annals of Probability
- Ann. Probab.
- Volume 45, Number 5 (2017), 3145-3201.
Invariant measure for the stochastic Navier–Stokes equations in unbounded 2D domains
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.
Ann. Probab., Volume 45, Number 5 (2017), 3145-3201.
Received: February 2015
Revised: June 2016
First available in Project Euclid: 23 September 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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