Global convergence of a two-fluid non-isentropic Euler–Poisson system in one space dimension

Abstract

In this paper, we study the global in time quasi-neutral limit for a two-fluid non-isentropic Euler–Poisson system in one space dimension. We prove that the system converges to the non-isentropic Euler equations as the Debye length tends to zero. This problem is studied for smooth solutions near the constant equilibrium state. To prove this result, we establish uniform energy estimates and various dissipation estimates with respect to the Debye length and the time. These estimates allow to pass to the limit to obtain the limit system by compactness arguments. In addition, the global convergence rate is obtained by use of stream function technique.