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

TY - JOUR

T1 - Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains

AU - Brzezniak, Zdzislaw

AU - Motyl, Elżbieta

AU - Ondrejat, Martin

N1 - © 2016, Institute of Mathematical Statistics. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - {invariant measure

KW - bw-Feller semigroup

KW - stochastic Navier-Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=85029852622&partnerID=8YFLogxK

U2 - 10.1214/16-AOP1133

DO - 10.1214/16-AOP1133

M3 - Article

SN - 0091-1798

VL - 45

SP - 3145

EP - 3201

JO - Annals of Probability

JF - Annals of Probability

IS - 5

M1 - AOP1133

ER -