Zero-electron-mass limit for Euler–Poisson system in a bounded domain

Abstract

In this paper, we study the zero-electron-mass limit of Euler–Poisson system in a bounded domain with an insulating boundary condition. The limit was only verified for the domain with no boundary in previous works. By approximation techniques, we establish the local well-posedness of classical solutions to the initial boundary value problem in the mixed space–time Sobolev space for the fixed parameter. Then, the local convergence of the system to the incompressible Euler equations with damping is proved rigorously for general initial data. Furthermore, the global convergence of smooth solutions is also justified for small initial data.