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

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Given constant data of density ρ₀, velocity -u₀ eᵣ, pressure p₀ and electric force -E₀ eᵣ 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 u₀>0, E₀>0, and that E₀ is sufficiently large depending on (ρ₀, u₀, p₀) and the length of the nozzle.