Large deviations for the Navier–Stokes equations driven by a white-in-time noise
Annales Henri Lebesgue, Volume 2 (2019), pp. 481-513.

Keywords Stochastic Navier–Stokes system, large deviations principle, occupation measures, multiplicative ergodicity

### Abstract

In this paper, we consider the 2D Navier–Stokes system driven by a white-in-time noise. We show that the occupation measures of the trajectories satisfy a large deviations principle, provided that the noise acts directly on all Fourier modes. The proofs are obtained by developing an approach introduced previously for discrete-time random dynamical systems, based on a Kifer-type criterion and a multiplicative ergodic theorem.

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