[Problème de Cauchy sur un cône caractéristique pour le système Einstein–Vlasov : (I) contraintes initiales]
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.
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@article{CRMATH_2017__355_2_187_0,
author = {Patenou, Jean Baptiste},
title = {Cauchy problem on a characteristic cone for the {Einstein{\textendash}Vlasov} system: {(I)} {The} initial data constraints},
journal = {Comptes Rendus. Math\'ematique},
pages = {187--192},
publisher = {Elsevier},
volume = {355},
number = {2},
year = {2017},
doi = {10.1016/j.crma.2016.11.018},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2016.11.018/}
}
TY - JOUR AU - Patenou, Jean Baptiste TI - Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints JO - Comptes Rendus. Mathématique PY - 2017 SP - 187 EP - 192 VL - 355 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2016.11.018/ DO - 10.1016/j.crma.2016.11.018 LA - en ID - CRMATH_2017__355_2_187_0 ER -
%0 Journal Article %A Patenou, Jean Baptiste %T Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints %J Comptes Rendus. Mathématique %D 2017 %P 187-192 %V 355 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2016.11.018/ %R 10.1016/j.crma.2016.11.018 %G en %F CRMATH_2017__355_2_187_0
Patenou, Jean Baptiste. Cauchy problem on a characteristic cone for the Einstein–Vlasov system: (I) The initial data constraints. Comptes Rendus. Mathématique, Tome 355 (2017) no. 2, pp. 187-192. doi : 10.1016/j.crma.2016.11.018. http://www.numdam.org/articles/10.1016/j.crma.2016.11.018/
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