具有球面集中非线性的三维 NLS 方程的适定性
偏微分方程分析
2024-01-02 v2 数学物理
泛函分析
math.MP
摘要
我们讨论具有集中于 上的非线性的三维 NLS 方程的强局部与全局适定性。确切地说，对任意 幂次非线性证明了局部适定性，而在小初值情形或在某些增长假设下的散焦情形获得了全局适定性。与文献中广泛研究的点集中 NLS 模型相比，此处非线性支撑的维数不允许直接推广已知技术，因而需要新的思路。
引用
@article{arxiv.2209.13504,
title = {Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity},
author = {Domenico Finco and Lorenzo Tentarelli and Alessandro Teta},
journal= {arXiv preprint arXiv:2209.13504},
year = {2024}
}
备注
40 pages. Keywords: NLS equation, concentrated nonlinearity, unit sphere, well-posedness, spherical harmonics. Minor changes have been made with respect to the previous version