# Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation

2 IPSO - Invariant Preserving SOlvers
IRMAR - Institut de Recherche Mathématique de Rennes, Inria Rennes – Bretagne Atlantique
Abstract : We are dealing with the validity of a large deviation principle for the two-dimensional Navier-Stokes equation, with periodic boundary conditions, perturbed by a Gaussian random forcing. We are here interested in the regime where both the strength of the noise and its correlation are vanishing, on a length scale $\e$ and $\d(\e)$, respectively, with $0<\e,\ \d(\e)<<1$. Depending on the relationship between $\e$ and $\d(\e)$ we will prove the validity of the large deviation principle in different functional spaces.
Type de document :
Article dans une revue
Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2019, 55 (1), pp.211-236. 〈10.1214/17-AIHP881〉
Domaine :

https://hal.archives-ouvertes.fr/hal-01287049
Contributeur : Marie-Annick Guillemer <>
Soumis le : vendredi 11 mars 2016 - 16:58:57
Dernière modification le : jeudi 7 février 2019 - 17:34:21

### Citation

Sandra Cerrai, Arnaud Debussche. Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2019, 55 (1), pp.211-236. 〈10.1214/17-AIHP881〉. 〈hal-01287049〉

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