Large deviations principle via Malliavin calculus for the Navier-Stokes system driven by a degenerate white-in-time noise
Probability
2022-02-01 v1 Analysis of PDEs
Abstract
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 arXiv:1410.6188 in a discrete-time setting and extended in arXiv:1505.03686 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.
Keywords
Cite
@article{arxiv.2201.12977,
title = {Large deviations principle via Malliavin calculus for the Navier-Stokes system driven by a degenerate white-in-time noise},
author = {Vahagn Nersesyan and Xuhui Peng and Lihu Xu},
journal= {arXiv preprint arXiv:2201.12977},
year = {2022}
}