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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

This paper concerns the existence of transonic shock solutions to the 2-D steady compressible Euler system in an almost flat finite nozzle ( in the sense that it is a generic small perturbation of a flat one ), under physical boundary…

Analysis of PDEs · Mathematics 2019-08-08 Beixiang Fang , Zhouping Xin

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

This paper is devoted to the structural stability of a transonic shock passing through a flat nozzle for two-dimensional steady compressible flows with an external force. We first establish the existence and uniqueness of one dimensional…

Analysis of PDEs · Mathematics 2026-01-14 Shangkun Weng , Wengang Yang

This paper concerns with the existence of transonic shocks for steady Euler flows in a 3-D axisymmetric cylindrical nozzle, which are governed by the Euler equations with the slip boundary condition on the wall of the nozzle and a receiver…

Analysis of PDEs · Mathematics 2020-09-30 Beixiang Fang , Xin Gao

We establish the existence and uniqueness of the transonic shock solution for steady isentropic Euler system with an external force in a rectangular cylinder under the three-dimensional perturbations for the incoming supersonic flow, the…

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

In this paper, we are trying to show the uniqueness of transonic shock solutions in an expanding nozzle under certain conditions and assumptions on the boundary data and the shock solution. The idea is to compare two transonic shock…

Analysis of PDEs · Mathematics 2025-02-11 Beixiang Fang , Xin Gao , Wei Xiang

This paper concerns the existence and location of three-dimensional axisymmetric transonic shocks with large swirl velocity for shock solutions of the steady compressible full Euler system in a cylindrical nozzle with prescribed receiver…

Analysis of PDEs · Mathematics 2026-01-22 Beixiang Fang , Xin Gao , Wei Xiang , Qin Zhao

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

We prove the stability of three-dimensional axisymmetric solutions to the steady Euler system with transonic shocks in divergent nozzles under perturbations of the exit pressure and the supersonic solution in the upstream region. We first…

Analysis of PDEs · Mathematics 2024-07-30 Hyangdong Park

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

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to…

Analysis of PDEs · Mathematics 2015-05-19 Tao Luo , Jeffrey Rauch , Chunjing Xie , Zhouping Xin

The existence and stability of a spherical transonic shock in a hemispherical shell under the three dimensional perturbations of the incoming flows and the exit pressure is established without any further restrictions on the background…

Analysis of PDEs · Mathematics 2025-03-20 Shangkun Weng

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure.…

Analysis of PDEs · Mathematics 2015-05-18 Myoungjean Bae , Mikhail Feldman

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock past a curved wedge for the steady full Euler equations in an important physical regime, which form a nonlinear system of…

Analysis of PDEs · Mathematics 2017-01-02 Gui-Qiang Chen , Jun Chen , Mikhail Feldman

We prove global in time dynamical stability of steady transonic shock solutions in divergent quasi-one-dimensional nozzles. We assume neither the smallness of the relative slope of the nozzle nor the weakness of the shock. Key ingredients…

Analysis of PDEs · Mathematics 2011-08-01 Jeffrey Rauch , Chunjing Xie , Zhouping Xin

We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are…

Analysis of PDEs · Mathematics 2010-04-13 Beixiang Fang , Li Liu , 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

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

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
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