{
  "id": "math/9807090",
  "version": "v1",
  "published": "1998-07-17T00:46:53.000Z",
  "updated": "1998-07-17T00:46:53.000Z",
  "title": "Persistence of invariant manifolds for nonlinear PDEs",
  "authors": [
    "Don A. Jones",
    "Steve Shkoller"
  ],
  "comment": "LaTeX2E, 32 pages, to appear in Studies in Applied Mathematics",
  "categories": [
    "math.AP",
    "math.DS",
    "math.NA"
  ],
  "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 $C^1$ 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",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-07-17T00:46:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K50",
      "58B99",
      "76D05"
    ],
    "keywords": [
      "nonlinear pdes",
      "invariant manifolds",
      "persistence",
      "two-dimensional navier-stokes equation",
      "infinite-dimensional hilbert manifold"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......7090J"
    }
  }
}