Global solutions for the one dimensional water-bag model

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 where the particle density has 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. Here we analyze the case of weak and strong solutions for the effective equations satisfied by the end-points and the electric field (water-bag model) in the relativistic setting. © 2009 International Press.