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We consider the stability of transonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle. This is the first work on the mixed-type problem of transonic flows across a contact…

Analysis of PDEs · Mathematics 2021-08-31 Feimin Huang , Jie Kuang , Dehua Wang , Wei Xiang

In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value…

Analysis of PDEs · Mathematics 2018-04-16 Feimin Huang , Jie Kuang , Dehua Wang , Wei Xiang

In this paper, we establish the existence and uniqueness of subsonic flows with a contact discontinuity in a two-dimensional finitely long slightly curved nozzle by prescribing the entropy, the Bernoulli's quantity and the horizontal mass…

Analysis of PDEs · Mathematics 2024-04-08 Shangkun Weng , Zihao Zhang

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 are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of…

Analysis of PDEs · Mathematics 2012-04-10 Gui-Qiang Chen , Xuemei Deng , Wei Xiang

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

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

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

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic…

Analysis of PDEs · Mathematics 2026-02-27 Dehua Wang , Tian-Yi Wang , Weiqiang Wang

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…

Analysis of PDEs · Mathematics 2015-07-28 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang

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

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the $n$-dimensional$(n\geq 2)$ Euler equations for steady irrotational flow that may contain stagnation points. This compactness…

Analysis of PDEs · Mathematics 2015-03-19 Feimin Huang , Tianyi Wang , Yong Wang

We prove the unique existence of supersonic solutions of the Euler- Poisson system for potential flow in a three-dimensional rectangular cylinder when prescribing the velocity and the strength of electric field at the entrance. Overall, the…

Analysis of PDEs · Mathematics 2021-03-03 Myoungjean Bae , Hyangdong Park

In this paper, we prove the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit…

Analysis of PDEs · Mathematics 2020-02-14 Shangkun Weng , Chunjing Xie , Zhouping Xin

We proved uniqueness and instability of the symmetric subsonic--sonic flow solution of the compressible potential flow equation in a surface with convergent areas of cross--sections. Such a surface may be regarded as an approximation of a…

Analysis of PDEs · Mathematics 2009-09-15 Pan Liu , Hairong Yuan

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…

Analysis of PDEs · Mathematics 2019-02-19 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang , Wei Xiang

We address the existence and stability of transonic shocks for the two-dimensional steady rotating Euler system in an almost flat nozzle. Under the influence of the Coriolis force, we first establish a class of special transonic shock…

Analysis of PDEs · Mathematics 2026-04-21 Zihao Zhang

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by…

Analysis of PDEs · Mathematics 2023-08-08 Shangkun Weng , Zihao Zhang

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles which are periodic in $x_1$ direction with the period $L$. It is shown that when the variation of Bernoulli function at some given…

Analysis of PDEs · Mathematics 2011-02-01 Chao Chen , Chunjing Xie

We established the existence, uniqueness and stability of subsonic flows past an airfoil with a vortex line at the trailing edge. Such a flow pattern is governed by the two dimensional steady compressible Euler equations. The vortex line…

Analysis of PDEs · Mathematics 2020-08-18 Jun Chen , Zhouping Xin , Aibin Zang