Supersonic Euler-Poisson flows in divergent nozzles

Abstract

This paper concerns the steady Euler-Poisson system in a two-dimensional divergent nozzle of finite length. The structural stability of supersonic potential flows for the Euler-Poisson system is transformed into the well-posedness of a second order quasilinear hyperbolic-elliptic coupled system with nonlinear boundary conditions. The well-posedness and the nonlinear structural stability of such supersonic flows under perturbations of boundary conditions are established by combining the iteration method with the estimates for hyperbolic-elliptic system.