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A Stochastic Nonlinear Schrödinger Equation¶with Multiplicative Noise

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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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Authors and Affiliations

  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.fr, France

    A. de Bouard & A. Debussche

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  1. A. de Bouard
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  2. A. Debussche
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Received: 21 December 1998 / Accepted: 22 February 1999

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de Bouard, A., Debussche, A. A Stochastic Nonlinear Schrödinger Equation¶with Multiplicative Noise. Commun. Math. Phys. 205, 161–181 (1999). https://doi.org/10.1007/s002200050672

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  • DOI: https://doi.org/10.1007/s002200050672

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