GLOBAL QUASI-NEUTRAL LIMIT FOR A TWO-FLUID EULER-POISSON SYSTEM IN SEVERAL SPACE DIMENSIONS

This paper concerns the quasi-neutral limit to the Cauchy problem for a two-fluid Euler-Poisson system in several space dimensions. When the initial data are sufficiently close to constant equilibrium states, we prove the global existence of smooth solutions with uniform bounds with respect to the Debye length in Sobolev spaces. This allows us to pass to the limit in the system for all times to obtain a compressible Euler system. We also prove global error estimates between the solution of the two-fluid Euler-Poisson system and that of the compressible Euler system. These results are obtained by establishing uniform energy estimates and various dissipation estimates. A key step in the proof is the control of the quasi-neutrality of the velocities. For this purpose, an orthogonal projection operator is used.