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arXiv · 1707.05610

Martingale solutions for the stochastic nonlinear Schr\"odinger equation in the energy space

Zdzislaw Brzezniak·Fabian Hornung·Lutz Weis
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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 $H^1$ on compact manifolds and bounded domains. We construct a martingale solution using a modified Faedo-Galerkin-method based on the Littlewood-Paley-decomposition. For 2d manifolds with bounded geometry, we use Strichartz estimates to show pathwise uniqueness.

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Zdzislaw Brzezniak, Fabian Hornung, Lutz Weis. 2017-07-18. Martingale solutions for the stochastic nonlinear Schr\"odinger equation in the energy space. https://arxiv.org/abs/1707.05610

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