Long time behavior of stochastic NLS with a small multiplicative noise

2021/11/14 by Chenjie Fan, Fan, Chenjie, Weijun Xu +3 · 1 citation
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2111.07212

openalex publication_date 2021/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the global space-time bound for the mass critical nonlinear Schrödinger equation perturbed by a small multiplicative noise in dimension three. The associated scattering behavior are also obtained. We also prove a global Strichartz space-time bound for the linear stochastic model, which is new itself and serves a prototype model for the nonlinear case. The proof combines techniques from \citefan2018global, \citefan2020long as well as local smoothing estimates for linear Schrödinger operators.

Citations

• Decay estimates for Schrödinger operators
• On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise

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• Nonlinear Schrödinger equation with Ornstein-Uhlenbeck operator

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