Radial transonic shock solutions of Euler-Poisson system in convergent nozzles

Abstract

Given constant data of density ${\rho }_0$, velocity $-u_0{\mathbf{e}}_r$, pressure $p_0$ and electric force $-E_0{\mathbf{e}}_r$ for supersonic flow at the entrance, and constant pressure $p_{\mathrm{ex}}$ for subsonic flow at the exit, we prove that Euler-Poisson system admits a unique transonic shock solution in a two dimensional convergent nozzle, provided that $u_0>0$, $E_0>0$, and that $E_0$ is sufficiently large depending on $({\rho }_0,u_0,p_0)$ and the length of the nozzle.