RADIAL TRANSONIC SHOCK SOLUTIONS OF EULER-POISSON SYSTEM IN CONVERGENT NOZZLES

Abstract

Given constant data, of density rho(0), velocity -u(0)e(r), pressure rho(0) and electric force -E(0)e(r) for supersonic flow at the entrance, and constant pressure p(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 (p(0), u(0),p(0)) and the length of the nozzle.