Comptes Rendus
Partial differential equations/Mathematical physics
Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints
[Problème de Cauchy sur un cône caractéristique pour le système Einstein–Vlasov : (I) contraintes initiales]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 187-192.

Dans cet article, on considère le problème de Cauchy caractéristique sur un cône pour le système des équations d'Einstein–Vlasov en jauge temporelle. On met en évidence les contraintes dépendant de la jauge, qui ensemble avec les contraintes hamiltoniennes et impulsionnelles constituent l'ensemble des équations des contraintes pour le cadre considéré. On étudie la résolution globale de ces équations à partir de certaines données indépendantes, le comportement des données initiales ainsi déduites au voisinage du sommet du cône et la préservation de la jauge.

In this paper, one considers a Cauchy problem with data on a characteristic cone for the Einstein–Vlasov system in temporal gauge. One highlights gauge-dependent constraints that, supplemented by the standard constraints i.e. the Hamiltonian and the momentum constraints, define the full set of constraints for the considered setting. One studies their global resolution from a suitable choice of some free data, the behavior of the deduced initial data at the vertex of the cone, and the preservation of the gauge.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.11.018

Jean Baptiste Patenou 1

1 Department of Mathematics and Computer Science, Faculty of Science, University of Dschang, P.O. Box. 67, Dschang, Cameroon
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Jean Baptiste Patenou. Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 187-192. doi : 10.1016/j.crma.2016.11.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.018/

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