Large deviations for the Navier–Stokes equations driven by a white-in-time noise

Nersesyan, Vahagn

Annales Henri Lebesgue, Tome 2 (2019), pp. 481-513.

Dans cet article, nous étudions le système de Navier–Stokes en dimension deux perturbé par un bruit blanc en temps. Nous montrons un principe de grandes déviations pour les mesures empiriques des trajectoires sous l’hypothèse que tous les modes de Fourier sont excités par le bruit. La preuve utilise une approche introduite précédemment pour des systèmes dynamiques aléatoires à temps discret, basée sur un critère de type Kifer et un théorème ergodique multiplicatif.

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.

Classification : 35Q30, 60B12, 60F10, 37H15
Mots clés : Stochastic Navier–Stokes system, large deviations principle, occupation measures, multiplicative ergodicity

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