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The Einstein Evolution Equations as a First-Order Quasi-Linear Symmetric Hyperbolic System, I

Fischer, Arthur E. and Marsden, Jerrold E. (1972) The Einstein Evolution Equations as a First-Order Quasi-Linear Symmetric Hyperbolic System, I. Communications in Mathematical Physics, 28 (1). pp. 1-38. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20100805-105052295

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Abstract

A systematic presentation of the quasi-linear first order symmetric hyperbolic systems of Friedrichs is presented. A number of sharp regularity and smoothness properties of the solutions are obtained. The present paper is devoted to the case of R n with suitable asymptotic conditions imposed. As an example, we apply this theory to give new proofs of the existence and uniqueness theorems for the Einstein equations in general relativity, due to Choquet-Bruhat and Lichnerowicz. These new proofs usingfirst order techniques are considerably simplier than the classical proofs based onsecond order techniques. Our existence results are as sharp as had been previously known, and our uniqueness results improve by one degree of differentiability those previously existing in the literature.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF02099369DOIUNSPECIFIED
http://www.springerlink.com/content/713g1g5x46470046/?p=890c944c73ae42eaaeb6726c89017f15&pi=3PublisherUNSPECIFIED
Additional Information:© by Springer-Verlag 1972. Received January 25: in revised form May 4, 1972. Partially supported by AEC Contract AT(04-3)-34. Partially Supported by NSF Contract GP-8257. We thank H. Brezis. Y. Choquct-Bruhat. M. Cantor. D. Ebin. K. O. Friedrichs. T. Kato. H. Kiinzlc. P. Lux. H. Levy. A. Lichnerowicz. M. Protter. R. Sachs. and A. Taub for several helpful discussions.
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Funding AgencyGrant Number
AECAT(04-3)-34
NSFGP-8257
Record Number:CaltechAUTHORS:20100805-105052295
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100805-105052295
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19293
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:05 Aug 2010 18:43
Last Modified:26 Dec 2012 12:17

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