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arXiv · 1201.0049

Rough solutions of Einstein vacuum equations in CMCSH gauge

Qian Wang
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Abstract

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 $\Box_\bg ϕ=0$ directly.

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Qian Wang. 2011-12-30. Rough solutions of Einstein vacuum equations in CMCSH gauge. https://arxiv.org/abs/1201.0049

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