波导 $\mathbb{R}^2$ $\times$ $\mathbb{T}^2$ 上散焦立方薛定谔方程的全局适定性与散射
偏微分方程分析
2019-11-04 v2
摘要
我们考虑 上散焦立方非线性薛定谔方程的大数据散射问题。该方程在能量与质量层面均为临界。关键要素包含全局时间 Stricharz 估计、共振系统近似与轮廓分解。假设二维立方共振系统的大数据散射成立,我们可证明该问题的大数据散射。
引用
@article{arxiv.1710.09702,
title = {Global well-posedness and scattering for the defocusing cubic Schr\"odinger equation on waveguide $\mathbb{R}^2$ $\times$ $\mathbb{T}^2$},
author = {Zehua Zhao},
journal= {arXiv preprint arXiv:1710.09702},
year = {2019}
}
备注
40 pages. The author used a compact template which may be better with no big changes. It will appear in Journal of Hyperbolic Differential Equations. arXiv admin note: substantial text overlap with arXiv:1205.6132, arXiv:1101.4527 by other authors