From Vlasov-Poisson system to the incompressible Euler system

This paper is devoted to the proof of the convergence of the Vlasov-Poisson system to the incompressible Euler equations in the so-called quasi-neutra l regime for cold electrons. The convergence is global in time and for gene ral initial data as long as a strong solution for the Euler system is known to exist. This investigation extends the results of Y. Brenier [1] where t he case of "well-prepared" initial data was handled.