Partial Differential Equations/Mathematical Physics
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.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.08.018
Patenou, Jean Baptiste 1

1 Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
@article{CRMATH_2011__349_19-20_1053_0,
     author = {Patenou, Jean Baptiste},
     title = {Characteristic {Cauchy} problem for the {Einstein} equations with {Vlasov} and {Scalar} matters in arbitrary dimension},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1053--1058},
     publisher = {Elsevier},
     volume = {349},
     number = {19-20},
     year = {2011},
     doi = {10.1016/j.crma.2011.08.018},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2011.08.018/}
}
TY  - JOUR
AU  - Patenou, Jean Baptiste
TI  - Characteristic Cauchy problem for the Einstein equations with Vlasov and Scalar matters in arbitrary dimension
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 1053
EP  - 1058
VL  - 349
IS  - 19-20
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2011.08.018/
DO  - 10.1016/j.crma.2011.08.018
LA  - en
ID  - CRMATH_2011__349_19-20_1053_0
ER  - 
%0 Journal Article
%A Patenou, Jean Baptiste
%T Characteristic Cauchy problem for the Einstein equations with Vlasov and Scalar matters in arbitrary dimension
%J Comptes Rendus. Mathématique
%D 2011
%P 1053-1058
%V 349
%N 19-20
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2011.08.018/
%R 10.1016/j.crma.2011.08.018
%G en
%F CRMATH_2011__349_19-20_1053_0
Patenou, Jean Baptiste. 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. http://www.numdam.org/articles/10.1016/j.crma.2011.08.018/

[1] Caciotta, G.; Nicolò, F. Global characteristic problem for Einstein Vacuum equations with small initial data (I): The initial data constraints, JHDE, Volume 2 (2005) no. 1, pp. 201-277

[2] Cagnac, F.; Choquet-Bruhat, Y.; Noutchegueme, N. General Relativity and Gravitational Physics (Bruzzo, U.; Cianci, R.; Massa, E., eds.), World Scientific, Singapore, 1987

[3] Choquet-Bruhat, Y. Problème de Cauchy pour le système intégro différentiel dʼEinstein–Liouville, Annales de lʼInstitut Fourier, Volume 21 (1971) no. 3, pp. 181-201

[4] Choquet-Bruhat, Y.; Noutchegueme, Norbert Système de Yang–Mills–Vlasov en jauge temporelle, Annales de lʼInstitut Henri Poincaré, Volume 55 (1991) no. 3, pp. 759-787

[5] Klainerman, S.; Nicolò, F. The Evolution Problem in General Relativity, Progress in Mathematical Physics, Birkhäuser, 2003

[6] J.B. Patenou, Doctorat/PhD thesis, University of Yaounde I (Cameroon), in preparation.

[7] Rendall, A.D. Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations, Proc. Roy. Soc. Lond. A, Volume 427 (1990), pp. 221-239

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

Cited by Sources: