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Communications in Mathematical Physics

, Volume 205, Issue 1, pp 161–181 | Cite as

A Stochastic Nonlinear Schrödinger Equation¶with Multiplicative Noise

  • A. de Bouard
  • A. Debussche
Article

Abstract:

We study a conservative stochastic nonlinear Schrödinger equation with a multiplicative noise. We show the global existence and uniqueness of square integrable solutions for subcritical nonlinearities, the critical exponent being the same, in dimension 1 or 2, as the critical exponent of the deterministic equation.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • A. de Bouard
    • 1
  • A. Debussche
    • 1
  1. 1.{Laboratoire d'Analyse Numérique et EDP, CNRS et Université Paris Sud, Bâtiment 425, 91405 Orsay,¶France. E-mail: anne.bouard@math.u-psud.fr; arnaud.debusche@math.u-psud.frFrance

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