Brzezniak, Zdzislaw orcid.org/0000-0001-8731-6523, Hornung, Fabian and Weis, Lutz (2019) Martingale solutions for the stochastic nonlinear Schrödinger equation in the energy space. Probability Theory and Related Fields. pp. 1273-1338. ISSN 1432-2064
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.
Metadata
Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2018 |
Keywords: | Compactness method, Galerkin approximation, Multiplicative noise, Nonlinear Schrödinger equation, Pathwise uniqueness |
Dates: |
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Institution: | The University of York |
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) |
Depositing User: | Pure (York) |
Date Deposited: | 17 Dec 2018 09:50 |
Last Modified: | 06 Jan 2024 00:36 |
Published Version: | https://doi.org/10.1007/s00440-018-0882-5 |
Status: | Published |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1007/s00440-018-0882-5 |
Related URLs: |
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