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

Vahagn Nersesyan; Meng Zhao

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arXiv · 2410.15727

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

Vahagn Nersesyan·Meng Zhao

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Abstract

We study the mixing properties of the white-forced Navier-Stokes system in the whole space $\mathbb{R}^2$. 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 Foia\c{s}-Prodi type estimate, weighted growth estimates for trajectories, and an estimate for the Leray projector involving Muckenhoupt $A_2$-class weights.

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Vahagn Nersesyan, Meng Zhao. 2024-10-21. Polynomial mixing for the white-forced Navier-Stokes system in the whole space. https://arxiv.org/abs/2410.15727

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