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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 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

This paper concerns the well-posedness of subsonic flows in a three-dimensional finitely long cylinder with arbitrary cross section. We establish the existence and uniqueness of subsonic flows in the Sobolev space by prescribing the normal…

Analysis of PDEs · Mathematics 2024-01-17 Shangkun Weng , Changkui Yao

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

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 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

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

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 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

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

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

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

In this paper, we are concerned with the two-dimensional steady supersonic combustion flows with a contact discontinuity moving through a nozzle of finite length. Mathematically, it can be formulated as a free boundary value problem…

Analysis of PDEs · Mathematics 2024-06-11 Junlei Gao , 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

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 are concerned with the global existence and stability of a smooth supersonic flow with vacuum state at infinity in a 3-D infinitely long divergent nozzle. The flow is described by a 3-D steady potential equation, which is…

Analysis of PDEs · Mathematics 2015-10-28 Xu Gang , Yin Huicheng

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

In this paper, we establish existence of global subsonic and subsonic-sonic flows through infinitely long axially symmetric nozzles by combining variational method, various elliptic estimates and a compensated compactness method. More…

Analysis of PDEs · Mathematics 2009-07-21 Chunjing Xie , Zhouping Xin