Rough solutions of Einstein vacuum equations in CMCSH gauge
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 wellposedness 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.
 Publication:

arXiv eprints
 Pub Date:
 December 2011
 arXiv:
 arXiv:1201.0049
 Bibcode:
 2012arXiv1201.0049W
 Keywords:

 Mathematics  Analysis of PDEs;
 General Relativity and Quantum Cosmology;
 Mathematics  Differential Geometry