Global solutions for the one dimensional Water-Bag model
Abstract
In this paper we study a special type of solution for the one dimensional Vlasov-Maxwell equations. We assume that initially the particle density is constant on its support in the phase space and we are looking for solutions with particle density having the same property at any time t > 0. More precisely, for each x the support of the density is assumed to be an interval [p,P] with end-points varying in space and time. We analyze here the case of weak and strong solutions for the effective equations verified by the end-points and the electric field (water-bag model) in the relativistic setting.
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