Work

Polynomial mixing for infinite-energy solutions of the white-forced Navier--Stokes equation in an infinite pipe

Year: 2026

Type: preprint

Abstract: We study the long-time behavior of the infinite-energy solutions to the white-forced Navier--Stokes equation in an infinite pipe $\mathbb{R}\times (-1,1)$ with no-slip boundary conditions. The equation is globally well-posed in uniformly local spaces satisfying the divergence-free condition. Under suitable degeneracy and spatial decay assumptions on the noise, we prove the uniqueness of the invariant measure and establish polynomial mixing in the dual-Lipschitz metric. This provides an affirmative answer to Open Problem 1 posed by Kuksin and Shirikyan \cite{KS17} in the case of zero cross-sectional flux.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15216

Author: Zhao, Meng

Institutions: Centre National de la Recherche Scientifique, CY Cergy Paris Université, Analyse, Géométrie et Modélisation

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, National Natural Science Foundation of China

Awards: G2325963797, Large-time dynamics of classical and quantum systems

OpenAlex ID: W7221746942

Cites: 3

Cited by:

Related to: 10