双曲 Schrödinger 方程的轮廓分解
偏微分方程分析
2020-08-24 v3
摘要
在本文中，我们证明了 上双曲 Schrödinger（或混合符号）方程在两种情况下的轮廓分解，一种为质量超临界，一种为质量临界。首先，作为热身，我们证明轮廓分解适用于 临界问题，这给出了例如 Fanelli-Visciglia (2013) 中结果之一的简单推广。然后，我们通过证明改进的 Strichartz 估计，给出了质量临界情况下轮廓分解的推导。我们将采用与 Killip-Visan (2008) 的笔记中非常相似的方法，但为了适应混合符号问题中出现的额外标度对称性，我们不得不进行双重 Whitney 分解。
引用
@article{arxiv.1708.08014,
title = {The profile decomposition for the hyperbolic Schr\"odinger equation},
author = {Benjamin Dodson and Jeremy L. Marzuola and Benoit Pausader and Daniel Spirn},
journal= {arXiv preprint arXiv:1708.08014},
year = {2020}
}
备注
Version 2 includes comments from an anonymous referee in particular with properly citing the proof of a similar estimate by Rogers and Vargas in Ref. 24. Ver. 3 contains a corrected version of the Appendix on Strichartz Extremizers thanks to Carneiro-Oliveira-Sousa in arXiv:1911.11796 (they are not Gaussians!). An Erratum is submitted to the journal version to note this as well