Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a Poincar´e-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron-Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brze´zniak and Li who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. who proved existence of a unique attractor for the time-dependent deterministic Navier-Stokes equations