[Équations de champs conformes d’Einstein couplées à de la matière de Vlasov sans masse]
Nous prouvons la stabilité de l’espace-temps de de Sitter, solution du système d’Einstein–Vlasov avec des particules sans masse. Nous considérons également la stabilité semi-globale de l’espace-temps de Minkowski pour le même système. La preuve de la stabilité repose sur l’usage de techniques conformes, et plus précisément les équations de champs conformes d’Einstein introduites par Friedrich. Nous exploitons l’invariance conforme de l’équation de Vlasov sans masse et adaptons le résultat d’existence locale en temps suffisamment long de Kato au système d’Einstein–Vlasov.
We prove the stability of de Sitter space-time as a solution to the Einstein–Vlasov system with massless particles. The semi-global stability of Minkowski space-time is also addressed. The proof relies on conformal techniques, namely Friedrich’s conformal Einstein field equations. We exploit the conformal invariance of the massless Vlasov equation on the cotangent bundle and adapt Kato’s local existence theorem for symmetric hyperbolic systems to prove a long enough time of existence for solutions of the evolution system implied by the Vlasov equation and the conformal Einstein field equations.
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Keywords: Einstein conformal field equations, stability problems, symmetric hyperbolic system, Vlasov equation
Mot clés : équation de champs conformes d’Einstein, problème de stabilité, systèmes symétrique hyperbolique, équation de Vlasov
@article{AIF_2021__71_2_799_0,
author = {Joudioux, J\'er\'emie and Thaller, Maximilian and Valiente Kroon, Juan A.},
title = {The conformal {Einstein} field equations with massless {Vlasov} matter},
journal = {Annales de l'Institut Fourier},
pages = {799--842},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {71},
number = {2},
year = {2021},
doi = {10.5802/aif.3414},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.3414/}
}
TY - JOUR AU - Joudioux, Jérémie AU - Thaller, Maximilian AU - Valiente Kroon, Juan A. TI - The conformal Einstein field equations with massless Vlasov matter JO - Annales de l'Institut Fourier PY - 2021 SP - 799 EP - 842 VL - 71 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.3414/ DO - 10.5802/aif.3414 LA - en ID - AIF_2021__71_2_799_0 ER -
%0 Journal Article %A Joudioux, Jérémie %A Thaller, Maximilian %A Valiente Kroon, Juan A. %T The conformal Einstein field equations with massless Vlasov matter %J Annales de l'Institut Fourier %D 2021 %P 799-842 %V 71 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.3414/ %R 10.5802/aif.3414 %G en %F AIF_2021__71_2_799_0
Joudioux, Jérémie; Thaller, Maximilian; Valiente Kroon, Juan A. The conformal Einstein field equations with massless Vlasov matter. Annales de l'Institut Fourier, Tome 71 (2021) no. 2, pp. 799-842. doi : 10.5802/aif.3414. http://www.numdam.org/articles/10.5802/aif.3414/
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