Scattering below the ground state for the 2D non-linear Schr\"{o}dinger and Klein-Gordon equations revisited
Abstract
We revisit the scattering problems for the 2D mass super-critical Schr\"{o}dinger and Klein-Gordon equations with radial data below the ground state in the energy space. We give an alternative proof of energy scattering for both defocusing and focusing cases using the ideas of Dodson-Murphy \citep{dodson2017new-radial}. Our results also include the exponential type nonlinearities which seems to be new for the focusing exponential NLS.
Keywords
Cite
@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}
}
Comments
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