Elliptic-hyperbolic systems and the Einstein equations
广义相对论与量子宇宙学
2007-05-23 v3 偏微分方程分析
摘要
The Einstein evolution equations are studied in a gauge given by a combination of the constant mean curvature and spatial harmonic coordinate conditions. This leads to a coupled quasilinear elliptic--hyperbolic system of evolution equations. We prove that the Cauchy problem is locally strongly well--posed and that a continuation principle holds. For initial data satisfying the Einstein constraint and gauge conditions, the solutions to the elliptic-hyperbolic system defined by the gauge fixed Einstein evolution equations are shown to give vacuum spacetimes.
关键词
引用
@article{arxiv.gr-qc/0110111,
title = {Elliptic-hyperbolic systems and the Einstein equations},
author = {Lars Andersson and Vincent Moncrief},
journal= {arXiv preprint arXiv:gr-qc/0110111},
year = {2007}
}
备注
29 pages, several minor corrections, submitted to Ann. H. Poincare