Smooth stable and unstable manifolds for stochastic partial differential equations
Dynamical Systems
2019-08-15 v1 Analysis of PDEs
Abstract
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations. We first show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron's method. Then, we prove the smoothness of these invariant manifolds.
Cite
@article{arxiv.math/0409483,
title = {Smooth stable and unstable manifolds for stochastic partial differential equations},
author = {Jinqiao Duan and Kening Lu and Bjorn Schmalfuss},
journal= {arXiv preprint arXiv:math/0409483},
year = {2019}
}