A sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates

• 成果类型: Article
• 署名作者: Ettinger, Boris; Lindblad, Hans
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.185.1.6
• 发表日期: 2017
• 页码: 311-330
• 关键词: vacuum equations

摘要

We are concerned with how regular initial data have to be to ensure local existence for Einstein's equations in wave coordinates. Klainerman-Rodnianski and Smith-Tataru showed that there in general is local existence for data in Sobolev spaces H<^>s with regularity s>2. We give an example of data in Sobolev spaces with regularity s=2 for which there is no local solution in this space.