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-neutral regime for cold electrons. The convergence is global in time and for general 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 the case of “well-prepared” initial data was handled.