Martingale solutions for the stochastic nonlinear Schr\"odinger equation in the energy space
Probability
2018-10-17 v2 Analysis of PDEs
Abstract
We consider a stochastic nonlinear Schr\"odinger equation with multiplicative noise in an abstract framework that covers subcritical focusing and defocusing stochastic NLS in on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo-Galerkin-method based on the Littlewood-Paley-decomposition. For 2d manifolds with bounded geometry, we use Strichartz estimates to show pathwise uniqueness.
Keywords
Cite
@article{arxiv.1707.05610,
title = {Martingale solutions for the stochastic nonlinear Schr\"odinger equation in the energy space},
author = {Zdzislaw Brzezniak and Fabian Hornung and Lutz Weis},
journal= {arXiv preprint arXiv:1707.05610},
year = {2018}
}
Comments
Accepted for publication in Probability Theory and Related Fields