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

Meng Zhao

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arXiv · 2610.15216

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

Meng Zhao

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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.

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BibTeX RIS

Meng Zhao. 2026-10-10. Polynomial mixing for infinite-energy solutions of the white-forced Navier--Stokes equation in an infinite pipe. https://arxiv.org/abs/2610.15216

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