Convergence of a non-isentropic Euler–Poisson system for all time

Abstract

We consider periodic smooth solutions for a non-isentropic Euler–Poisson system with small parameters, in which the momentum and energy equations are partially dissipative. When initial data are close to constant equilibrium states, we prove the global-in-time convergence of the system as parameters go to zero. The limit systems are incompressible Euler equations with dissipation, the drift-diffusion system and the energy-transport system. The proof of the results is based on compactness arguments and uniform energy estimates with respect to the time and the parameters.