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arXiv · 1603.05167

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

Boris Ettinger·Hans Lindblad
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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.

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Boris Ettinger, Hans Lindblad. 2016-03-16. A sharp counterexample to local existence of low regularity solutions to Einstein's equations in wave coordinates. https://arxiv.org/abs/1603.05167

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