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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

We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this…

Analysis of PDEs · Mathematics 2025-01-28 Xiaomin Zhang , Peng Qu , Huimin Yu

This paper concerns the structural stability of smooth cylindrically symmetric supersonic Euler-Poisson flows in nozzles. Both three-dimensional and axisymmetric perturbations are considered. On one hand, we establish the existence and…

Analysis of PDEs · Mathematics 2025-03-21 Chunpeng Wang , Zihao Zhang

We establish the local uniqueness of steady transonic shock solutions with spherical symmetry for the three-dimensional full Euler equations. These transonic shock-fronts are important for understanding transonic shock phenomena in…

Analysis of PDEs · Mathematics 2011-12-09 Gui-Qiang G. Chen , Hairong Yuan

For a class of external forces, we prove the existence and uniqueness of smooth transonic flows to the one dimensional steady Euler system with an external force, which is subsonic at the inlet and flows out at supersonic speed after…

Analysis of PDEs · Mathematics 2024-03-26 Shangkun Weng , Yan Zhou

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 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

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…

Analysis of PDEs · Mathematics 2026-04-28 Yuanyuan Xing , Zihao Zhang

We establish the existence of an axisymmetric weak solution to the steady Euler system with a transonic shock, nonzero vorticity, and nonzero swirl in a three-dimensional cylinder. When prescribing the supersonic solution in the upstream…

Analysis of PDEs · Mathematics 2020-11-30 Hyangdong Park , Hyeongyu Ryu

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

For the three-dimensional steady non-isentropic compressible Euler system with friction, we show existence of a class of symmetric subsonic, supersonic and transonic-shock solutions in a straight duct with constant square-section. Such…

Analysis of PDEs · Mathematics 2018-11-02 Hairong Yuan , Qin Zhao

The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong…

Analysis of PDEs · Mathematics 2018-01-10 Gui-Qiang G. Chen , Jun Chen , Mikhail Feldman

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…

Analysis of PDEs · Mathematics 2026-05-01 Yuanyuan Xing , Zihao Zhang

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

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed…

Analysis of PDEs · Mathematics 2021-01-05 Shangkun Weng , Zhouping Xin , Hongwei Yuan

We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic…

Analysis of PDEs · Mathematics 2018-01-16 Min Ding , Hairong Yuan

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…

Analysis of PDEs · Mathematics 2016-03-16 Shangkun Weng

For an upstream supersonic flow past a straight-sided cone in $\R^3$ whose vertex angle is less than the critical angle, a transonic (supersonic-subsonic) shock-front attached to the cone vertex can be formed in the flow. In this paper we…

Analysis of PDEs · Mathematics 2016-03-15 Gui-Qiang Chen , Beixiang Fang

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