Persistence of invariant manifolds for nonlinear PDEs
Abstract
We prove that under certain stability and smoothing properties of the semi-groups generated by the partial differential equations that we consider, manifolds left invariant by these flows persist under perturbation. In particular, we extend well known finite-dimensional results to the setting of an infinite-dimensional Hilbert manifold with a semi-group that leaves a submanifold invariant. We then study the persistence of global unstable manifolds of hyperbolic fixed-points, and as an application consider the two-dimensional Navier-Stokes equation under a fully discrete approximation. Finally, we apply our theory to the persistence of inertial manifolds for those PDEs which possess them. te
Keywords
Cite
@article{arxiv.math/9807090,
title = {Persistence of invariant manifolds for nonlinear PDEs},
author = {Don A. Jones and Steve Shkoller},
journal= {arXiv preprint arXiv:math/9807090},
year = {2025}
}
Comments
LaTeX2E, 32 pages, to appear in Studies in Applied Mathematics