重温能量空间中基态下含径向数据的二维非线性薛定谔与 Klein-Gordon 方程的基态下散射
偏微分方程分析
2020-08-05 v4
摘要
我们重温能量空间中基态下含径向数据的二维质量超临界薛定谔与 Klein-Gordon 方程的散射问题。利用 Dodson-Murphy 的思想，我们对散焦与聚焦两种情形给出了能量散射的另一种证明。我们的结果也包含了指数型非线性，这对于聚焦指数型 NLS 而言似乎是新的。
引用
@article{arxiv.1906.01804,
title = {Scattering below the ground state for the 2D non-linear Schr\"{o}dinger and Klein-Gordon equations revisited},
author = {Zihua Guo and Jia Shen},
journal= {arXiv preprint arXiv:1906.01804},
year = {2020}
}
备注
24 pages; Some typos and improvement were made incorporating with the referee's report. To appear Journal of Mathematical Physics. We noticed that a recent manuscript arXiv:2006.08279v1 (Remark 1.13) had a question about our paper (on the virial-Morawetz estimates). After private communications, the question was clarified