Rough solutions of Einstein vacuum equations in CMCSH gauge

Details Rough solutions of Einstein vacuum equations in CMCSH gauge Rough solutions of Einstein vacuum equations in CMCSH gauge

2011-12-30

arxiv.org/abs/1201.0049v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric $\bg$, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $\Box_\bg \phi=0$ directly.

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