Subsonic Euler-Poisson flows with nonzero vorticity in convergent nozzles

TL;DR

This paper proves the existence, uniqueness, and stability of smooth subsonic Euler-Poisson flows with nonzero vorticity in convergent nozzles, using coordinate transformations and a deformation-curl-Poisson approach.

Contribution

It introduces a novel analysis framework for subsonic Euler-Poisson flows with vorticity in nozzle geometries, establishing well-posedness and structural stability.

Findings

Existence of radially symmetric subsonic solutions in convergent nozzles.

Uniqueness and regularity of solutions with nonzero vorticity.

Stability of solutions under boundary perturbations.

Abstract

This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions to the steady Euler-Poisson system. We then investigate the structural stability of these background subsonic flows under perturbations of suitable boundary conditions, and establish the existence and uniqueness of smooth subsonic Euler-Poisson flows with nonzero vorticity. The solution shares the same regularity for the velocity, the pressure, the entropy and the electric potential. The deformation-curl-Poisson decomposition is utilized to reformulate the steady Euler-Poisson system as a deformation-curl-Poisson system together with several transport equations. The key point lies on the analysis of the well-posedness of the boundary value problem for the associated linearized elliptic system, which is established by using a special structure of the system to derive a priori estimates.