On the stochastic nonlinear Schrödinger equations with nonsmooth additive noise

Tadahiro Oh; Oana Pocovnicu; Yuzhao Wang

doi:10.1215/21562261-2019-0060

Abstract

We study the stochastic nonlinear Schrödinger equations with additive stochastic forcing. By using the dispersive estimate, we present a simple argument, constructing a unique local-in-time solution with rougher stochastic forcing than those considered in the literature.

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Tadahiro Oh. Oana Pocovnicu. Yuzhao Wang. "On the stochastic nonlinear Schrödinger equations with nonsmooth additive noise." Kyoto J. Math. 60 (4) 1227 - 1243, December 2020. https://doi.org/10.1215/21562261-2019-0060

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Received: 17 May 2018; Revised: 10 September 2018; Accepted: 19 September 2018; Published: December 2020

First available in Project Euclid: 30 September 2020

MathSciNet: MR4175807

Digital Object Identifier: 10.1215/21562261-2019-0060

Subjects:

Primary: 35Q55 , 60H30

Keywords: dispersive estimate , stochastic nonlinear Schrödinger equation , well-posedness

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