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Random attractors

  • Hans Crauel
  • Arnaud Debussche
  • Franco Flandoli
Article

Abstract

In this paper, we generalize the notion of an attractor for the stochastic dynamical system introduced in [7]. We prove that the stochastic attractor satisfies most of the properties satisfied by the usual attractor in the theory of deterministic dynamical systems. We also show that our results apply to the stochastic Navier-Stokes equation, the white noise-driven Burgers equation, and a nonlinear stochastic wave equation.

Key words

Random attractors stochastic dynamical systems deterministic nonautonomous systems stochastic Navier-Stokes equation stochastic Burgers equation stochastic nonlinear wave equation 

AMS subject classifications

58F11 58F12 60H15 34D45 35Q30 35Q35 35L05 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Hans Crauel
    • 1
  • Arnaud Debussche
    • 2
  • Franco Flandoli
    • 3
  1. 1.SaarbrückenGermany
  2. 2.Laboratoire d'Analyse Numérique et CNRSUniversité Paris-SudOrsay CedexFrance
  3. 3.Dipartimento di Matematica Applicata U. DiniPisaItaly

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