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

Sandra Cerrai; Arnaud Debussche

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arXiv · 1603.02527

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

Sandra Cerrai·Arnaud Debussche

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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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Sandra Cerrai, Arnaud Debussche. 2016-03-08. Large deviations for the two-dimensional stochastic Navier-Stokes equation with vanishing noise correlation. https://arxiv.org/abs/1603.02527

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