Using ODE techniques we prove the existence of large classes of initial data satisfying the constraints for the spherically symmetric Einstein-Vlasov-Maxwell system. These include data for which the ratio of total charge to total mass is arbitrarily large.

Using the iterative scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.

We look for the global in time solution of the Cauchy problem corresponding to the asymptotically flat spherically symmetric E.V.M system with small initial data. Using an estimate, we also prove that if solution of the system stated above develops a singularity at all time, then the first one has to appear at the center of symmetry.

We prove local in time existence theorems of solutions of the Cauchy problem for the Yang-Mills system in temporal gauge, with current generated by a distribution function that satisfies a Vlasov equation, and an unknown non-abelian charge density subject to a conservation equation.Résumé. Nous démontrons des théorèmes d'existence locale dans le temps d'une solution du problème de Cauchy pour le système de Yang-Mills en jauge temporelle, dont le courant est engendré par une fonction de distribution satisfaisantà uneéquation de Vlasov, et une charge de jauge non-abelienne de densité inconnue soumiseà uneéquation de conservation.• On suppose que la charge de Yang-Mills q a une densité physique inconnue ρ, fonction réelle positive sur V ; ρ : V → R + .

We consider the VEM system in the context of spherical symmetry and we try to establish a global static solution with isotropic pressure that approaches Minkowski spacetime at infinity and have a regular center. To be in accordance with numerical investigation we take here low charge particles.