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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

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 construct a supersonic-sonic smooth patch solution for the two dimensional steady Euler equations in gas dynamics. This patch is extracted from the Frankl problem in the study of transonic flow with local supersonic bubble over an…

Analysis of PDEs · Mathematics 2021-01-05 Yanbo Hu , Jiequan Li

This article concerns the global-in-time existence of smooth solutions with small amplitude to two space dimensional Euler-Poisson system. The main difficulty lies in the slow time decay $(1+t)^{-1}$ of the linear system. Inspired by Ozawa,…

Analysis of PDEs · Mathematics 2015-05-30 Juhi Jang

We are concerned with the unique existence of an axisymmetric supersonic solution with nonzero vorticity and nonzero angular momentum density for the steady Euler-Poisson system in three-dimensional divergent nozzles when prescribing the…

Analysis of PDEs · Mathematics 2025-12-25 Hyangdong Park

This paper concerns the structural stability of supersonic flows with a contact discontinuity in a finitely long curved nozzle for the two-dimensional steady compressible rotating Euler system. Concerning the effect of Coriolis force, we…

Analysis of PDEs · Mathematics 2023-07-04 Shangkun Weng , Zihao Zhang

Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global non-isentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the…

Analysis of PDEs · Mathematics 2020-03-24 Geng Lai

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

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 consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

Analysis of PDEs · Mathematics 2025-06-23 Alex Doak , Karsten Matthies , Jonathan Sewell , Miles H. Wheeler

In this paper, we established the global existence of supersonic entropy solutions with a strong contact discontinuity over Lipschitz wall governed by the two-dimensional steady exothermically reacting Euler equations, when the total…

Analysis of PDEs · Mathematics 2017-09-12 Wei Xiang , Yongqian Zhang , Qin Zhao

We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler…

Analysis of PDEs · Mathematics 2007-10-22 Jun chen

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

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

This paper is concerned with the linear stability analysis for the Couette flow of the Euler-Poisson system for both ionic fluid and electronic fluid in the domain $\bb{T}\times\bb{R}$. We establish the upper and lower bounds of the…

Analysis of PDEs · Mathematics 2024-01-31 Xueke Pu , Wenli Zhou , Dongfen Bian

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

This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves for the two-dimensional full Euler equations in gas dynamics. In order to deal with the parabolic degeneracy near the sonic curve, a novel set of…

Analysis of PDEs · Mathematics 2019-10-23 Yanbo Hu , Jiequan Li

In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with {\it general} incoming horizontal velocity as long as the flux is larger than a critical value. One of the…

Analysis of PDEs · Mathematics 2024-02-23 Yan Li , Wenhui Shi , Lan Tang , Chunjing Xie

A recent prominent result asserts that steady incompressible Euler flows strictly away from stagnation in a two-dimensional infinitely long strip must be shear flows. On the other hand, flows with stagnation points, very challenging in…

Analysis of PDEs · Mathematics 2023-12-12 Congming Li , Yingshu Lv , Henrik Shahgholian , Chunjing Xie

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