Center manifolds for rough partial differential equations (Q6164915)

In this paper, the authors deal with the existence of center manifolds for stochastic partial differential equations with nonlinear drift driven by \(\gamma\)-Holder rough paths with \(\gamma \in ({\frac 13}, {\frac 12})\). The main result is proved by the Lyapunov-Perron method along with the rough paths theory and the semigroup theory. As an application, the authors show the existence of center manifolds for a class of reaction-diffusion equations and the Swift-Hohenberg equations.