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

Zdzislaw Brzezniak, Fabian Hornung, Lutz Weis

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)1273-1338
Number of pages66
JournalProbability Theory and Related Fields
Issue number3-4
Early online date1 Nov 2018
Publication statusPublished - 1 Aug 2019

Bibliographical note

© The Author(s) 2018


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

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