Polynomial mixing for the white-forced Navier-Stokes system in the whole space

2024/10/21 by Vahagn Nersesyan, Meng Zhao, Nersesyan, Vahagn +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2410.15727

openalex publication_date 2024/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the mixing properties of the white-forced Navier-Stokes system in the whole space ℝ². Assuming that the noise is sufficiently non-degenerate, we prove the uniqueness of stationary measure and polynomial mixing in the dual-Lipschitz metric. The proof combines the coupling method with a Foiaş-Prodi type estimate, weighted growth estimates for trajectories, and an estimate for the Leray projector involving Muckenhoupt A₂-class weights.

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