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

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...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 362; pp. 230 - 249
Main Authors Nersesyan, Vahagn, Peng, Xuhui, Xu, Lihu
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.07.2023
Elsevier
Subjects
Analysis of PDEs
Degenerate noise
Feynman–Kac semigroup
Large deviations
Malliavin calculus
Mathematics
Navier–Stokes system
Uniform Feller property
37H15
Navier–Stokes system
Uniform Feller property
60F10
60B12
93B05
Feynman–Kac semigroup
60H07
Degenerate noise
35Q30
Large deviations
Malliavin calculus
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2023.03.004