具有缓慢衰减势的聚焦三维立方NLS的动力学
偏微分方程分析
2018-12-04 v3
摘要
在本文中，我们考虑具有缓慢衰减势的三维立方聚焦非线性薛定谔方程(NLS)。采用Ibrahim-Masmoudi-Nakanishi的变分方法\cite{IMN}，我们得到了一个散射条件。该条件在某种意义下是尖锐的，因为若其不成立则解将爆破。爆破部分的证明依赖于Du-Wu-Zhang的方法\cite{DWZ}。
引用
@article{arxiv.1811.07578,
title = {Dynamics of the focusing 3D cubic NLS with slowly decaying potential},
author = {Qing Guo and Hua Wang and Xiaohua Yao},
journal= {arXiv preprint arXiv:1811.07578},
year = {2018}
}
备注
29 pages, This is a new version where the proof of Lemma 2.1 was added