在 $L^2$ 正则性下 $\mathbb{R}$ 上散焦质量临界随机非线性薛定谔方程的全局适定性
偏微分方程分析
2022-02-09 v1 概率论
摘要
我们证明了在 且 正则性下质量临界随机非线性薛定谔方程解的全局存在性与稳定性。我们的构造始于截断次临界问题解的存在性。在截断存在的前提下，我们将临界方程的解构造为次临界解的极限。随后我们得到截断临界问题解的一致界，使我们可以在极限中去掉截断。
引用
@article{arxiv.1810.07925,
title = {Global well-posedness for the defocusing mass-critical stochastic nonlinear Schr\"odinger equation on $\mathbb{R}$ at $L^2$ regularity},
author = {Chenjie Fan and Weijun Xu},
journal= {arXiv preprint arXiv:1810.07925},
year = {2022}
}
备注
37 pages. The material presented in this article is a re-orgasination of arXiv:1803.03257 and part of arXiv:1807.04402 of the authors. The other part of arXiv:1807.04402, which has not been covered in the current article, will be re-written as another independent one (forthcoming). Only the current article and the forthcoming one will be submitted for journal publication