Supersonic Euler-Poisson flows with nonzero vorticity in convergent nozzles

TL;DR

This paper proves the existence and stability of supersonic Euler-Poisson flows with nonzero vorticity in convergent nozzles, highlighting the electric field's stabilizing effect on the flow structure.

Contribution

It introduces a novel reformulation of the Euler-Poisson system and establishes the structural stability of supersonic flows under boundary perturbations.

Findings

Existence of radially symmetric supersonic flows in convergent nozzles.

Stability of these flows under multi-dimensional boundary perturbations.

Electric field force can counteract geometric effects and stabilize flow features.

Abstract

This paper concerns supersonic flows with nonzero vorticity governed by the steady Euler-Poisson system, under the coupled effects of the electric potential and the geometry of a convergent nozzle. By the coordinate rotation, the existence of radially symmetric supersonic flows is proved. We then establish the structural stability of these background supersonic flows under multi-dimensional perturbations of the boundary conditions. One of the crucial ingredients of the analysis is the reformulation of the steady Euler-Poisson system into a deformation-curl-Poisson system and several transport equations via the deformation-curl-Poisson decomposition. Another one is to obtain the well-posedness of the boundary value problem for the associated linearized hyperbolic-elliptic coupled system, which is achieved through a delicate choice of multiplier to derive a priori estimates. The result indicates that the electric field force in compressible flows can counteract the geometric effects of the convergent nozzle and thereby stabilize key physical features of the flow.