Rough Solutions of Einstein Vacuum Equations in CMCSH Gauge

@article{Wang2011RoughSO,
  title={Rough Solutions of Einstein Vacuum Equations in CMCSH Gauge},
  author={Qian Wang},
  journal={Communications in Mathematical Physics},
  year={2011},
  volume={328},
  pages={1275-1340}
}
  • Qian Wang
  • Published 30 December 2011
  • Mathematics
  • Communications in Mathematical Physics
In this paper, we consider very rough solutions to the Cauchy problem for the Einstein vacuum equations in CMC spatial harmonic gauge, and obtain the local well-posedness result in Hs, s > 2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric g, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $${\square_{\bf g} \phi=0}$$□gϕ=0 directly. 
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