Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
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| Format: | Preprint |
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2026
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| _version_ | 1866917260295143424 |
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| author | Luongo, Eliseo Triggiano, Francesco |
| author_facet | Luongo, Eliseo Triggiano, Francesco |
| contents | We study a slow-fast system of coupled two- and three-dimensional Navier-Stokes equations in which the fast component is perturbed by an additive fractional Brownian noise with Hurst parameter $H>\frac{1}{3}$. The system is analyzed using rough path theory, and the limiting behaviour strongly depends on the value of $H$. We prove convergence in law of the slow component to a Navier-Stokes system with an additional Itô-Stokes drift when $H<\frac{1}{2}$. In contrast, for $H\in (\frac{1}{2},1)$, the limit equation features only a transport noise driven by a rough path. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_08680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion Luongo, Eliseo Triggiano, Francesco Probability Analysis of PDEs We study a slow-fast system of coupled two- and three-dimensional Navier-Stokes equations in which the fast component is perturbed by an additive fractional Brownian noise with Hurst parameter $H>\frac{1}{3}$. The system is analyzed using rough path theory, and the limiting behaviour strongly depends on the value of $H$. We prove convergence in law of the slow component to a Navier-Stokes system with an additional Itô-Stokes drift when $H<\frac{1}{2}$. In contrast, for $H\in (\frac{1}{2},1)$, the limit equation features only a transport noise driven by a rough path. |
| title | Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2602.08680 |