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
.
Under a
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
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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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