渐近闵可夫斯基空间中辐射场的渐近行为
偏微分方程分析
2014-07-01 v4 微分几何
谱理论
摘要
我们考虑一个非捕获的n维洛伦兹流形，其末端结构模拟了闵可夫斯基空间的径向紧化。我们找到了在所有渐近区域中波动方程的缓增前向解的完整渐近展开。渐近展开中看到的衰减率与紧化“北帽”上的自然渐近双曲问题的共振有关。对于适合我们框架的闵可夫斯基空间的小扰动，我们展示了比Klainerman-Sobolev估计更好的衰减率。
引用
@article{arxiv.1212.5141,
title = {Asymptotics of radiation fields in asymptotically Minkowski space},
author = {Dean Baskin and András Vasy and Jared Wunsch},
journal= {arXiv preprint arXiv:1212.5141},
year = {2014}
}
备注
67 pages, 2 figures; version 2 was a substantial revision with the main result (Theorem 1.1) improved; version 3 fixes a minor error in the iterative argument establishing the asymptotic expansion; version 4 includes a few cosmetic changes and adds a few references