{
  "id": "math/0409483",
  "version": "v1",
  "published": "2004-09-24T19:17:32.000Z",
  "updated": "2004-09-24T19:17:32.000Z",
  "title": "Smooth stable and unstable manifolds for stochastic partial differential equations",
  "authors": [
    "Jinqiao Duan",
    "Kening Lu",
    "Bjorn Schmalfuss"
  ],
  "doi": "10.1007/s10884-004-7830-z",
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-24T19:17:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "37H05",
      "37L55",
      "37L25",
      "37D10"
    ],
    "keywords": [
      "stochastic partial differential equations",
      "unstable manifolds",
      "smooth stable",
      "random dynamical systems",
      "invariant manifolds"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Dynamics and Differential Equations",
      "year": 2004,
      "month": "Oct",
      "volume": 16,
      "number": 4,
      "pages": 949
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004JDDE...16..949D"
    }
  }
}