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

• 成果类型: Article
• 署名作者: Brzezniak, Zdzislaw; Hornung, Fabian; Weis, Lutz
• 署名单位: University of York - UK; Helmholtz Association; Karlsruhe Institute of Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0882-5
• 发表日期: 2019
• 页码: 1273-1338
• 关键词: weak solutions; inequalities; dispersion; Operators

摘要

We consider a stochastic nonlinear Schrodinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing Stochastic NLSE in H1 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.