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We show that for steady compressible potential flow in a class of straight divergent nozzles with arbitrary cross-section, if the flow is supersonic and spherically symmetric at the entry, and the given pressure (velocity) is appropriately…

Analysis of PDEs · Mathematics 2009-03-31 Li Liu , Hairong Yuan

Given constant data of density $\rho_0$, velocity $-u_0{\bf e}_r$, pressure $p_0$ and electric force $-E_0{\bf e}_r$ for supersonic flow at the entrance, and constant pressure $p_{\rm ex}$ for subsonic flow at the exit, we prove that…

Analysis of PDEs · Mathematics 2017-03-01 Myoungjean Bae , Yong Park

We establish the existence and stability of the transonic shock solution to three-dimensional axisymmetric Euler system with an external force in a cylinder under perturbations of the incoming supersonic flow, the exit pressure, the…

Analysis of PDEs · Mathematics 2026-05-26 Zihao Zhang

We develop a method that works in general product Riemannian manifold to decompose the three-dimensional steady full compressible Euler system, which is of elliptic-hyperbolic composite-mixed type for subsonic flows. The method is applied…

Analysis of PDEs · Mathematics 2015-05-13 Li Liu , Gang Xu , Hairong Yuan

We establish the existence and stability of cylindrical transonic shock solutions under three dimensional perturbations of the incoming flows and the exit pressure without any further restrictions on the background transonic shock…

Analysis of PDEs · Mathematics 2024-01-23 Shangkun Weng , Zhouping Xin

This paper concerns the existence of transonic shocks for steady exothermically reacting Euler flows in an almost flat nozzle with the small rate of the exothermic reaction. One of the key points is to quantitatively determine the position…

Analysis of PDEs · Mathematics 2023-01-02 Beixiang Fang , Piye Sun , Qin Zhao

We prove the global uniqueness of multidimensional subsonic flows for the steady Euler--Poisson system in a bounded nozzle in the sense that uniqueness holds without restricting solutions to be small perturbations of a background state. The…

Analysis of PDEs · Mathematics 2026-04-28 Myoungjean Bae , Ben Duan , Chunjing Xie

We establish the stability of 3-D axisymmetric transonic shock solutions of the steady full Euler system in divergent nozzles under small perturbations of an incoming radial supersonic flow and a constant pressure at the exit of the…

Analysis of PDEs · Mathematics 2021-02-26 Yong Park

This paper concerns studies on smooth transonic flows with nonzero vorticity in De Laval nozzles for a quasi two dimensional steady Euler flow model which is a generalization of the classical quasi one dimensional model. First, the…

Analysis of PDEs · Mathematics 2024-05-29 Shangkun Weng , Zhouping Xin

In this paper, we prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed…

Analysis of PDEs · Mathematics 2013-09-16 Myoungjean Bae , Ben Duan , Chunjing Xie

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence…

Analysis of PDEs · Mathematics 2015-06-11 Gui-Qiang G. Chen , Vaibhav Kukreja , Hairong Yuan

We investigate two dimensional steady Euler-Poisson system which describe the motion of compressible self-gravitating flows. The unique existence and stability of subsonic flows in a duct of finite length are obtained when prescribing the…

Analysis of PDEs · Mathematics 2014-06-18 Myoungjean Bae , Ben Duan , Chunjing Xie

In this paper, we are concerned with the existence of transonic shock solutions for two-dimensional (2-d) steady Euler flows of polytropic gases with the vertical gravity in a horizontal nozzle under a pressure condition imposed at the exit…

Analysis of PDEs · Mathematics 2025-04-08 Beixiang Fang , Xin Gao , Wei Xiang , Qin Zhao

For a supersonic Euler flow past a straight wedge whose vertex angle is less than the extreme angle, there exists a shock-front emanating from the wedge vertex, and the shock-front is usually strong especially when the vertex angle of the…

Analysis of PDEs · Mathematics 2007-05-23 Gui-Qiang Chen , Tian-Hong Li

In this paper we are concerned with the existence of transonic shocks for 2-D steady isothermal Euler flows in a horizontal flat nozzle under vertical gravity. In particular, we focus on the contribution of the vertical gravity in…

Analysis of PDEs · Mathematics 2021-12-07 Beixiang Fang , Xin Gao

For unipolar hydrodynamic model of semiconductor device represented by Euler-Poisson equations, when the doping profile is supersonic, the existence of steady transonic shock solutions and C-smooth steady transonic solutions for…

Analysis of PDEs · Mathematics 2022-02-09 Yue-Hong Feng , Ming Mei , Guojing Zhang

In this paper, both smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder are studied. We first establish the existence of cylindrically symmetric smooth subsonic and transonic flows to steady…

Analysis of PDEs · Mathematics 2023-08-23 Shangkun Weng , Wengang Yang , Na Zhang

We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are…

Analysis of PDEs · Mathematics 2021-05-25 Gui-Qiang G. Chen , Jie Kuang , Yongqian Zhang

When an upstream steady uniform supersonic flow impinges onto a symmetric straight-sided wedge, governed by the Euler equations, there are two possible steady oblique shock configurations if the wedge angle is less than the detachment angle…

Analysis of PDEs · Mathematics 2019-01-18 Gui-Qiang G. Chen

In this paper, we study the existence and uniqueness of three dimensional steady Euler flows in rectangular nozzles when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the…

Analysis of PDEs · Mathematics 2013-05-13 Chao Chen , Chunjing Xie