Title: Rough analysis of two scale systems Show Chinese title

Title: 两尺度系统的粗略分析

Abstract: We address a slow-fast system of coupled three dimensional Navier--Stokes equations where the fast component is perturbed by an additive Brownian noise. By means of the rough path theory, we establish the convergence in law of the slow component towards a Navier--Stokes system with an It{\^o}--Stokes drift and a rough path driven transport noise. This gives an alternative, more general and direct proof to \cite{DP22}. Notably, the limiting rough path is identified as a geometric rough path, which does not necessarily coincide with the Stratonovich lift of the Brownian motion. Show Chinese abstract

Abstract: 我们研究了一个三维耦合的慢速-快速Navier-Stokes方程系统，其中快变量受到加性Brown运动的扰动。 通过粗糙路径理论，我们证明了慢变量在分布意义下收敛到一个带有Itô-Stokes漂移和由粗糙路径驱动的输运噪声的Navier-Stokes系统。 这为\cite{DP22}提供了一种更通用且直接的替代证明。 值得注意的是，极限粗糙路径被识别为一个几何粗糙路径，它不一定与Brown运动的Stratonovich提升相一致。