On steady subsonic flows for Euler-Poisson models

TL;DR

This paper investigates the structural stability of steady subsonic solutions in the Euler-Poisson system, demonstrating stability under small perturbations when the Mach number and electric field are low, using a novel elliptic system formulation.

Contribution

It introduces a new formulation of Euler-Poisson equations utilizing Bernoulli's law to reduce velocity dimension and proves stability with respect to various small perturbations.

Findings

Proven stability of subsonic solutions under small perturbations.

Developed a new elliptic system with oblique and Dirichlet boundary conditions.

Reduced velocity field dimension via Bernoulli's law.

Abstract

In this paper, we are concerned with the structural stability of some steady subsonic solutions for Euler-Poisson system. A steady subsonic solution with subsonic background charge is proven to be structurally stable with respect to small perturbations of the background charge, the incoming flow angles, the normal electric field and the Bernoulli's function at the inlet and the end pressure at the exit, provided the background solution has a low Mach number and a small electric field. Following the idea developed in [19], we give a new formulation for Euler-Poisson equations, which employ the Bernoulli's law to reduce the dimension of the velocity field. The new ingredient in our mathematical analysis is the solvability of a new second order elliptic system supplemented with oblique derivative conditions at the inlet and Dirichlet boundary conditions at the exit of the nozzle.