Large deviations principle via Malliavin calculus for the Navier-Stokes system driven by a degenerate white-in-time noise
Résumé
The purpose of this paper is to establish the Donsker-Varadhan type large deviations principle (LDP) for the two-dimensional stochastic Navier-Stokes system. The main novelty is that the noise is assumed to be highly degenerate in the Fourier space. The proof is carried out by using a criterion for the LDP developed in [JNPS18] in a discrete-time setting and extended in [MN18] to the continuous-time. One of the main conditions of that criterion is the uniform Feller property for the Feynman-Kac semigroup, which we verify by using Malliavin calculus.
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