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In this paper we discuss global existence of the solution of the Maxwell andNewton system of equations, describing the interaction of a rigid chargedistribution with the electromagnetic field it generates. A unique solution isproved to exist (for regular charge distributions) on suitable homogeneous andnon-homogeneous Sobolev spaces, for the electromagnetic field, and oncoordinate and velocity space for the charge; provided initial data belong tothe subspace that satisfies the divergence part of Maxwell's equations.

Global Solution of the Electromagnetic Field-Particle System of Equations