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September 2017 Invariant measure for the stochastic Navier–Stokes equations in unbounded 2D domains
Zdzisław Brzeźniak, Elżbieta Motyl, Martin Ondrejat
Ann. Probab. 45(5): 3145-3201 (September 2017). DOI: 10.1214/16-AOP1133


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.


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Zdzisław Brzeźniak. Elżbieta Motyl. Martin Ondrejat. "Invariant measure for the stochastic Navier–Stokes equations in unbounded 2D domains." Ann. Probab. 45 (5) 3145 - 3201, September 2017.


Received: 1 February 2015; Revised: 1 June 2016; Published: September 2017
First available in Project Euclid: 23 September 2017

zbMATH: 06812202
MathSciNet: MR3706740
Digital Object Identifier: 10.1214/16-AOP1133

Primary: 35Q30 , 37L40 , 60H15
Secondary: 60J25 , 76M35

Keywords: $bw$-Feller semigroup , invariant measure , stochastic Navier–Stokes equations

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 5 • September 2017
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