Subsonic Euler-Poisson flows with nonzero vorticity in convergent nozzles

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.