Electron. J. Diff. Equ., Vol. 2011 (2011), No. 163, pp. 1-22.

Goursat problem for the Yang-Mills-Vlasov system in temporal gauge

Marcel Dossa, Marcel Nanga

Abstract:
This article studies the characteristic Cauchy problem for the Yang-Mills-Vlasov (YMV) system in temporal gauge, where the initial data are specified on two intersecting smooth characteristic hypersurfaces of Minkowski spacetime $(\mathbb{R}^{4},\eta )$. Under a $\mathcal{C}^{\infty }$ hypothesis on the data, we solve the initial constraint problem and the evolution problem. Local in time existence and uniqueness results are established thanks to a suitable combination of the method of characteristics, Leray's Theory of hyperbolic systems and techniques developed by Choquet-Bruhat for ordinary spatial Cauchy problems related to (YMV) systems.

Submitted July 16, 2010. Published December 13, 2011.
Math Subject Classifications: 81Q13, 35L45,35L55.
Key Words: Goursat problem; characteristic initial hypersurfaces; Yang-Mills-Vlasov system; temporal gauge; initial constraints; evolution problem.

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Marcel Dossa
Université de Yaoundé I, Faculté des Sciences
B.P. 812, Yaoundé, Cameroun
email: marceldossa@yahoo.fr
Marcel Nanga
Université de N'Djaména
Faculté des Sciences Exactes et Appliquées
B.P. 1027, N'Djaména, Tchad
email: marnanga@yahoo.fr

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