Averaging principle for slow-fast SPDEs driven by mixed noises

This paper investigates a class of slow-fast stochastic partial differential equations driven by fractional Brownian motion and standard Brownian motion. Firstly, the well-posedness for such equations are established. Secondly, we provide the uniform $L_p$-estimation for slow variable relying on the mild stochastic sewing Lemma. Finally, we obtain the approximate solution for slow variable via averaging principle.