Geodesic
A sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates
Boris Ettinger ; Hans Lindblad1
1 Johns Hopkins University, Baltimore, MD
Annals of mathematics, Tome 185 (2017) no. 1, pp. 311-330.

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We give a sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates. We show that there are initial data in $H^2$ satisfying the wave coordinate condition such that there is no solution in $H^2$ to Einstein equations in wave coordinates for any positive time. This result is sharp since Klainerman-Rodnianski and Smith-Tataru proved existence for the same equations with slightly more regular initial data.
DOI : 10.4007/annals.2017.185.1.6

Boris Ettinger  ; Hans Lindblad 1

1 Johns Hopkins University, Baltimore, MD 
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Boris Ettinger; Hans Lindblad. A sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates. Annals of mathematics, Tome 185 (2017) no. 1, pp. 311-330. doi : 10.4007/annals.2017.185.1.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.1.6/

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