From two-fluid Euler–Poisson equations to one-fluid Euler equations

Abstract

We consider quasi-neutral limits in two-fluid isentropic Euler–Poisson equations arising in the modeling of unmagnetized plasmas and semiconductors. For periodic smooth solutions, we justify an asymptotic expansion in a time interval independent of the Debye length. This implies the convergence of the equations to compressible Euler equations. The proof is based on energy estimates for symmetrizable hyperbolic equations and on the exploration of the coupling between the Euler equations and the Poisson equation.