Characteristic Cauchy problem for the Einstein equations with Vlasov and Scalar matters in arbitrary dimension

Jean Baptiste Patenou

doi:10.1016/j.crma.2011.08.018

Partial Differential Equations/Mathematical Physics

Characteristic Cauchy problem for the Einstein equations with Vlasov and Scalar matters in arbitrary dimension
[Problème de Cauchy caractéristique pour les équations dʼEinstein–Vlasov–Champ Scalaire en dimension quelconque]

Présenté par : Yvonne Choquet-Bruhat

Jean Baptiste Patenou ¹

¹ Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1053-1058.

Résumé
Abstract

On établit et résout sur la réunion de deux hypersurfaces caractéristiques régulières sécantes, un système hiérarchisé dʼéquations des contraintes compatibles avec la preuve dʼun théorème dʼexistence pour les équations dʼEinstein–Vlasov–Champ Scalaire en jauge temporelle.

We derive and solve on two null intersecting smooth hypersurfaces, a set of hierarchical constraints equations, suitable with the proof of an existence theorem for the Einstein equations with Vlasov and Scalar matters, in temporal gauge.

Reçu le : 2011-06-23
Accepté le : 2011-08-23
Publié le : 2011-09-25

DOI : 10.1016/j.crma.2011.08.018

Affiliations des auteurs :

Jean Baptiste Patenou ¹

¹ Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

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     author = {Jean Baptiste Patenou},
     title = {Characteristic {Cauchy} problem for the {Einstein} equations with {Vlasov} and {Scalar} matters in arbitrary dimension},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1053--1058},
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     language = {en},
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Jean Baptiste Patenou. Characteristic Cauchy problem for the Einstein equations with Vlasov and Scalar matters in arbitrary dimension. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1053-1058. doi : 10.1016/j.crma.2011.08.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.018/

Bibliographie
Cité par

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[8] Oscar Reula Strongly hyperbolic systems in general relativity, JHDE, Volume 1 (2004) no. 2, pp. 251-269

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