A sharp counterexample to local existence of low regularity solutions to Einstein's equations in wave coordinates
Analysis of PDEs
2016-09-19 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.1603.05167,
title = {A sharp counterexample to local existence of low regularity solutions to Einstein's equations in wave coordinates},
author = {Boris Ettinger and Hans Lindblad},
journal= {arXiv preprint arXiv:1603.05167},
year = {2016}
}