Subsonic Solutions for the Multidimensional Euler-Poisson System of Plasma

In this study, we investigate the steady Euler-Poisson system that governs the dynamics of a collisionless ion-electron plasma. We establish the unique existence and structural stability of subsonic potential flow in a multidimensional nozzle. This is accomplished by prescribing the electric potential difference on a noninsulated boundary from a fixed point at the exit, along with specifying the pressure at the exit. The Euler-Poisson system is reformulated into a second-order quasilinear elliptic system, and the key ingredient of the analysis is to gain the C1,alpha$$ {C}<^>{1,\alpha } $$ estimate of the corresponding linearized system.