含与不含表面张力的二维水波问题在弧长表述下非线性薛定谔近似的有效性
偏微分方程分析
2020-11-06 v2
摘要
我们考虑无限长有限深度 canal 中带与不带表面张力的二维水波问题。为描述该问题的小振荡波包状解的包络演化，可形式化推导非线性薛定谔方程作为近似方程。近年来，多位作者已对无表面张力情形证明了该近似的有效性。在本文中，我们通过证明在二维水波问题弧长表述下物理相关时间跨度上的误差估计，严格证明了带与不带表面张力情形的非线性薛定谔近似的有效性。该误差估计关于表面张力的强度是一致均匀的，当波包高度与表面张力趋于零时亦如此。
引用
@article{arxiv.1907.03014,
title = {Validity of the Nonlinear Schr\"odinger Approximation for the Two-Dimensional Water Wave Problem With and Without Surface Tension in the Arc Length Formulation},
author = {Wolf-Patrick Düll},
journal= {arXiv preprint arXiv:1907.03014},
year = {2020}
}
备注
This paper is a minor revision of the previous submission arXiv:1907.03014v1. In its present form, the paper has been accepted for publication in Archive for Rational Mechanics and Analysis