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Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space

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JournalProbability Theory and Related Fields
DateAccepted/In press - 20 Oct 2018
DateE-pub ahead of print (current) - 1 Nov 2018
Number of pages66
Early online date1/11/18
Original languageEnglish

Abstract

We consider a stochastic nonlinear Schrödinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H 1 on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo–Galerkin-method based on the Littlewood–Paley-decomposition. For the 2d manifolds with bounded geometry, we use the Strichartz estimates to show the pathwise uniqueness of solutions.

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© The Author(s) 2018

    Research areas

  • Compactness method, Galerkin approximation, Multiplicative noise, Nonlinear Schrödinger equation, Pathwise uniqueness

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