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Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion
Eliseo Luongo, Francesco Triggiano · 2026-02-09 · via math.PR updates on arXiv.org

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.

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