Abstract
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.
Citation
Boris Ettinger. Hans Lindblad. "A sharp counterexample to local existence of low regularity solutions to Einstein equations in wave coordinates." Ann. of Math. (2) 185 (1) 311 - 330, January 2017. https://doi.org/10.4007/annals.2017.185.1.6
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