Long time behavior of stochastic NLS with a small multiplicative noise
Analysis of PDEs
2021-12-21 v2 Probability
Abstract
We prove the global space-time bound for the mass critical nonlinear Schr\"odinger 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 \cite{fan2018global}, \cite{fan2020long} as well as local smoothing estimates for linear Schr\"odinger operators.
Keywords
Cite
@article{arxiv.2111.07212,
title = {Long time behavior of stochastic NLS with a small multiplicative noise},
author = {Chenjie Fan and Weijun Xu and Zehua Zhao},
journal= {arXiv preprint arXiv:2111.07212},
year = {2021}
}
Comments
We include the scattering behavior in this revision and all non endpoint Strichartz type bound are now included for nonlinear model. 28 pages, no figures, all comments are welcome