The hydrodynamical limit of the Vlasov-Poisson system

For an ensemble of particles with selfconsistent interaction we consider two models of the matter for describing the time evolution of the system: the kinetic and the fluid model given by the Vlasov-Poisson system and the Euler-Poisson system with pressure zero. Suppose that in the kinetic description velocities initially concentrate. We then show that velocities also concentrate for later times. In the hydrodynamical limit this concentration represents a solution of the fluid dynamical model.