Vanishing electron mass limit in the bipolar Euler–Poisson system

The bipolar Euler–Poisson system in physics consists of the conservation laws for the electron and ion densities and their current densities, coupled with the Poisson equation for the electrostatic potential. The limit of vanishing ratio of the electron mass to the ion mass in the nn-dimensional flat torus is proved in the case of well prepared initial data. The limiting system is composed of two separated equations, where the equation for electron is the incompressible Euler equation with damping, which means physically that the evolution for electrons and ions can be treated as separated motions in the small ratio case.