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Elliptic-hyperbolic systems and the Einstein equations | | Lars Andersson
; Vincent Moncrief
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25 Oct 2001 | | Journal: | Annales Henri Poincare 4 (2003) 1-34 | | Subject: | General Relativity and Quantum Cosmology; Analysis of PDEs | gr-qc math.AP | | Affiliation: | University of Miami), Vincent Moncrief (Yale University | | Abstract: | 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. | | Source: | arXiv, gr-qc/0110111 | | Services: | Forum | Review | PDF | Favorites | |
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