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Article Dans Une Revue Journal of Differential Equations Année : 2023

Large deviations principle via Malliavin calculus for the Navier–Stokes system driven by a degenerate white-in-time noise

Xuhui Peng
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Lihu Xu
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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 [17] in a discrete-time setting and extended in [26] 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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Dates et versions

hal-04106293 , version 1 (06-06-2023)

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Citer

Vahagn Nersesyan, Xuhui Peng, Lihu Xu. Large deviations principle via Malliavin calculus for the Navier–Stokes system driven by a degenerate white-in-time noise. Journal of Differential Equations, 2023, 362, pp.230-249. ⟨10.1016/j.jde.2023.03.004⟩. ⟨hal-04106293⟩

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