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

TL;DR

This paper proves the existence of an invariant measure for stochastic 2D Navier-Stokes equations with multiplicative noise in unbounded domains, extending previous results from additive noise cases and addressing an open problem.

Contribution

It establishes the invariant measure existence for stochastic 2D Navier-Stokes equations with multiplicative noise in unbounded domains, building on recent work on related stochastic PDEs.

Findings

Existence of invariant measure proven for stochastic Navier-Stokes in unbounded domains.

Extension from additive to multiplicative noise cases.

Addresses an open problem in the mathematical analysis of stochastic fluid dynamics.

Abstract

Building upon a recent work by two of the authours 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 authour and Y. Li proved a corresponding result in the case of an additive noise.