Averaging Dynamics and Wong-Zakai approximations for a Fast-Slow Navier-Stokes System Driven by fractional Brownian Motion

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.

💡 Research Summary

The paper investigates a coupled fast‑slow Navier‑Stokes system in two or three spatial dimensions, where the fast component is driven by an additive fractional Brownian motion (fBm) with Hurst parameter (H>1/3). The authors consider the system

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