Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 163, pp. 1-22.
Title: Goursat problem for the Yang-Mills-Vlasov system
in temporal gauge
Authors: Marcel Dossa (Univ. de Yaounde I, Cameroun)
Marcel Nanga (Univ. de N'Djamena, Tchad)
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.