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We study stochastic partial differential equations (SPDEs) with potentiallyvery rough fractional noise with Hurst parameter $H\in(0,1)$. Close to a changeof stability measured with a small parameter $\varepsilon$, we rely on thenatural separation of time-scales and establish a simplified description of theessential dynamics. We prove that up to an error term bounded by a power of$\varepsilon$ depending on the Hurst parameter we can approximate the solutionof the SPDE in first order by an SDE, the so called amplitude equation, and insecond order by a fast infinite dimensional Ornstein-Uhlenbeck process. To thisaim we need to establish an explicit averaging result for stochastic integralsdriven by rough fractional noise for small Hurst parameters.

Amplitude equations for SPDEs driven by fractional additive noise with small Hurst parameter