Global Quasi-Neutral Limit for a Two-Fluid Euler–Poisson System in Several Space Dimensions

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