带小乘性噪声的随机NLS的长时间行为
偏微分方程分析
2021-12-21 v2 概率论
摘要
我们证明了三维质量临界非线性Schrödinger方程在小的乘性噪声扰动下的全局时空界。相应的散射行为也得到了证明。我们还证明了线性随机模型的全局Strichartz时空界，这本身是新结果并作为非线性情形的原型模型。证明结合了来自\cite{fan2018global}、\cite{fan2020long}的技术以及线性Schrödinger算子的局部光滑估计。
引用
@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}
}
备注
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