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

Myoungjean Bae, Yong Park
2018 Discrete and Continuous Dynamical Systems. Series S  
Given constant data of density ρ 0 , velocity −u 0 er, pressure p 0 and electric force −E 0 er for supersonic flow at the entrance, and constant pressure pex 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 (ρ 0 , u 0 , p 0 ) and the length of the nozzle. 2010 Mathematics Subject Classification. 34A12, 34A34, 76H05, 76L05, 76N10, 76X05.
doi:10.3934/dcdss.2018049 fatcat:xrm4lfikjncypa3qohku7imcxq