Level-3 large deviations for the white-forced 2D Navier-Stokes system in a bounded domain

2025/06/17 by Meng Zhao, Zhao, Meng
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2506.14119

openalex publication_date 2025/06/17 · openalex created_date 2025/10/18 · openalex updated_date 2026/07/28

Abstract

We study the large deviations principle (LDP) of Donsker-Varadhan type for the white-forced Navier-Stokes system in a bounded domain. Under the assumption that the noise is non-degenerate, we establish level-2 and level-3 LDPs with rate functions given by the Donsker-Varadhan formulas. The proof relies on an improved version of Kifer's criterion, a lift argument inspired from [DV83], an improved abstract result on the large-time asymptotics of generalized Markov semigroups, and a delicate approximation scheme utilizing the resolvent operators of the Markov semigroup.

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