Partial Differential Equations/Mathematical Physics
The Goursat problem for the Einstein–Vlasov system: (II) The evolution of initial data
Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 277-280.

We solve, locally in time, the evolution problem associated with the Einstein–Vlasov (EV) system, the initial data being specified on two intersecting smooth null hypersurfaces. The proof of the obtained result relies heavily on a fixed point method deployed in appropriate weighted Sobolev spaces. The main tools of this method consist of adequate Sobolev inequalities and Moser estimates combined with energy inequalities for first-order and second-order linear hyperbolic partial differential equations.

Nous résolvons, localement en temps, le problème de lʼévolution associé au système Einstein–Vlasov (EV), les données initiales étant portées par deux hypersurfaces caractéristiques régulières sécantes. La preuve du résultat obtenu repose essentiellement sur une méthode de point fixe déployée dans un cadre approprié dʼespaces de Sobolev à poids. Les principaux ingrédients de cette méthode sont constitués des inégalités de Sobolev et des estimations de Moser adéquates, combinées aux inégalités énergétiques pour les équations aux dérivées partielles hyperboliques linéaires du premier ordre et du second ordre.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.04.014
Tadmon, Calvin 1, 2

1 Department of Mathematics and Computer Science, University of Dschang, P.O. Box 67, Dschang, Cameroon
2 Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa
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Tadmon, Calvin. The Goursat problem for the Einstein–Vlasov system: (II) The evolution of initial data. Comptes Rendus. Mathématique, Volume 351 (2013) no. 7-8, pp. 277-280. doi : 10.1016/j.crma.2013.04.014. http://www.numdam.org/articles/10.1016/j.crma.2013.04.014/

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