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

TL;DR

This paper proves the existence of a unique random attractor for the stochastic 2D Navier-Stokes equations in certain unbounded domains, extending previous deterministic and asymptotic compactness results.

Contribution

It establishes the existence and uniqueness of a random attractor for stochastic 2D Navier-Stokes equations in unbounded domains, complementing prior deterministic and asymptotic results.

Findings

Existence of a unique random attractor for the stochastic flow.

Extension of deterministic attractor results to stochastic setting.

Generalization to unbounded 2D domains.

Abstract

We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincar\'e domain has a unique random attractor. This result complements a recent result by Brze\'zniak and Li [10] who showed that the flow is asymptotically compact and generalizes a recent result by Caraballo et al. [12] who proved existence of a unique pullback attractor for the time-dependent deterministic Navier-Stokes equations in a 2-dimensional Poincar\'e domain.