Unstable manifolds for rough evolution equations

Abstract

In this paper, we consider a class of evolution equations driven by finite-dimensional $\gamma$-Hölder rough paths, where $\gamma \in (1/3,1/2]$. We prove the global-in-time solutions of rough evolution equations(REEs) in a sutiable space, also obtain that the solutions generate random dynamical systems. Meanwhile, we derive the existence of local unstable manifolds for such equations by a properly discretized Lyapunov-Perron method.

arXiv admin note: text overlap with arXiv:1811.10037 by other authors