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

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.