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

Sandra Cerrai 1 Arnaud Debussche 2
2 MINGUS - Multi-scale numerical geometric schemes
IRMAR - Institut de Recherche Mathématique de Rennes, ENS Rennes - École normale supérieure - 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.
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Submitted on : Friday, March 11, 2016 - 4:58:57 PM
Last modification on : Friday, April 12, 2019 - 1:14:16 AM

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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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