temporal gauge — 1 articles found.

Cauchy Problem on Two Characteristic Hypersurfaces for the Einstein-Vlasov Scalar Field Equations in Temporal Gauge

C. R. Math. Rep. Acad. Sci. Canada Vol. 39 (2) 2017, pp. 45-59
Vol.39 (2) 2017
Marcel Dossa; Jean Baptiste Patenou Details
(Received: 2015-12-01 , Revised: 2016-05-16 )
(Received: 2015-12-01 , Revised: 2016-05-16 )

Marcel Dossa,University of Yaounde I, Faculty of Sciences, Department of Mathematics, P. O. Box. 812, Yaounde, Cameroon; e-mail: marceldossa@yahoo.fr

Jean Baptiste Patenou,University of Dschang, Faculty of Sciences, Department of Mathematics and Computer Science, P. O. Box. 67 Dschang, Cameroon
e-mail: jeanbaptiste.patenou@univ-dschang.org,jpatenou@yahoo.fr

Abstract/Résumé:

In this paper, we consider the initial value problem for the Einstein-Vlasov scalar field equations in temporal gauge, where the initial data are prescribed on two characteristic smooth intersecting hypersurfaces. From a suitable choice of some free data, the initial data constraints’s problem is solved globally, then the evolution problem relative to the deduced initial data is solved locally in time.

Dans cet article, on considère le problème de Cauchy pour les équations d’Einstein-Vlasov-Champ scalaire en jauge temporelle, dans le cas où les données initiales sont préscrites sur deux hypersurfaces caractéristiques régulières sécantes. A partir d’un choix judicieux de certaines données indépendantes, le problème des contraintes initiales est globalement résolu, et ensuite le problème de l’évolution relatif aux données initiales déduites est résolu localement dans le temps.

Keywords: Characteristic Cauchy problem, general relativity, geometric-transport scalar field equations, initial data constraints's problem, temporal gauge, well posedness

AMS Subject Classification: PDE in relativity, Einstein's equations (general structure; canonical formalism; Cauchy problems) 35Q75, 83C05

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