Averaging principle for slow-fast systems of PDEs with rough drivers

TL;DR

This paper develops an averaging principle for slow-fast rough PDE systems, proving strong convergence of the slow component to an averaged solution using controlled rough path theory and discretization methods.

Contribution

It introduces a novel averaging approach for rough PDEs with monotone interpolation spaces, extending classical methods to rough and infinite-dimensional settings.

Findings

Strong convergence of the slow component as ε → 0

Effective averaging technique for rough PDE systems

Framework applicable to monotone interpolation Hilbert spaces

Abstract

This paper investigates a class of slow--fast systems of rough partial differential equations defined over a monotone family of interpolation Hilbert spaces. By employing the controlled rough path framework tailored to a monotone family of interpolation spaces, together with a time discretization argument, we demonstrate that the slow component strongly converges to the solution of the averaged system in the supremum norm as the time-scale parameter $\varepsilon$ tends to $0$.