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Random attractors

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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.

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Authors and Affiliations

  1. Hellwigstraße 17, 66121, Saarbrücken, Germany

    Hans Crauel

  2. Laboratoire d'Analyse Numérique et CNRS, Université Paris-Sud, Batiment 425, 91405, Orsay Cedex, France

    Arnaud Debussche

  3. Dipartimento di Matematica Applicata U. Dini, Via Bonanno 25B, 56126, Pisa, Italy

    Franco Flandoli

Authors
  1. Hans Crauel
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  2. Arnaud Debussche
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  3. Franco Flandoli
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Crauel, H., Debussche, A. & Flandoli, F. Random attractors. J Dyn Diff Equat 9, 307–341 (1997). https://doi.org/10.1007/BF02219225

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  • DOI: https://doi.org/10.1007/BF02219225

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