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.
"Invariant measure for the stochastic Navier–Stokes equations in unbounded 2D domains." Ann. Probab. 45 (5) 3145 - 3201, September 2017. https://doi.org/10.1214/16-AOP1133