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Polynomial mixing for infinite-energy solutions of the white-forced Navier--Stokes equation in an infinite pipe
Abstract
We study the long-time behavior of the infinite-energy solutions to the white-forced Navier--Stokes equation in an infinite pipe ℝ× (−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
@misc{zhao2026polynomial,
title = {{Polynomial mixing for infinite-energy solutions of the white-forced Navier--Stokes equation in an infinite pipe}},
author = {Meng Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15216},
eprint = {2610.15216},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15216},
}
RIS
TY - UNPB
TI - Polynomial mixing for infinite-energy solutions of the white-forced Navier--Stokes equation in an infinite pipe
AU - Meng Zhao
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.15216
UR - https://arxiv.org/abs/2610.15216
AB - We study the long-time behavior of the infinite-energy solutions to the white-forced Navier--Stokes equation in an infinite pipe ℝ× (−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.
ER -