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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 are concerned with the well-posedness of an inverse problem for determining the wedge boundary and associated two-dimensional steady supersonic Euler flow past the wedge, provided that the pressure distribution on the boundary surface of…

Analysis of PDEs · Mathematics 2024-09-30 Gui-Qiang G. Chen , Yun Pu , Yongqian Zhang

In this paper, we investigate steady Euler flows in a two-dimensional bounded domain. By an adaption of the vorticity method, we prove that for any nonconstant harmonic function $q$, which corresponds to a nontrivial irrotational flow,…

Analysis of PDEs · Mathematics 2019-10-16 Daomin Cao , Guodong Wang , Zhan Weicheng

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

We study the motion of isentropic gas in nozzles. This is a major subject in fluid dynamics. In fact, the nozzle is utilized to increase the thrust of rocket engines. Moreover, the nozzle flow is closely related to astrophysics. These…

Analysis of PDEs · Mathematics 2017-02-21 Naoki Tsuge

We are concerned with the two-dimensional steady supersonic reacting Euler flow past Lipschitz bending walls that are small perturbations of a convex one, and establish the existence of global entropy solutions when the total variation of…

Analysis of PDEs · Mathematics 2016-11-15 Gui-Qiang Chen , Jie Kuang , Yongqian Zhang

We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in…

Numerical Analysis · Mathematics 2008-12-24 Dietmar Kroener , Philippe G. LeFloch , Mai-Duc Thanh

We are concerned with inverse problems for supersonic potential flows past infinite axisymmetric Lipschitz cones. The supersonic flows under consideration are governed by the steady isentropic Euler equations for axisymmetric potential…

Analysis of PDEs · Mathematics 2023-10-30 Gui-Qiang G. Chen , Yun Pu , Yongqian Zhang

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles…

Analysis of PDEs · Mathematics 2018-05-09 Gui-Qiang G. Chen , Matthew R. I. Schrecker

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

This paper considers the low Mach number limit and far field convergence rates of steady Euler flows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First, the well-posedness theory for both…

Analysis of PDEs · Mathematics 2020-04-30 Lei Ma , Tian-Yi Wang , Chunjing Xie

This paper concerns compressible subsonic jet flows for a given surrounding pressure from a two-dimensional finitely long convergent nozzle with straight solid wall, which are governed by a free boundary problem for a quasilinear elliptic…

Analysis of PDEs · Mathematics 2019-02-08 Chunpeng Wang , Zhouping Xin

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 are concerned with the global existence of entropy solutions of the two-dimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate…

Analysis of PDEs · Mathematics 2013-11-07 Gui-Qiang Chen , Changguo Xiao , Yongqian Zhang

We show existence, uniqueness and stability for a family of stationary subsonic compressible Euler flows with mass-additions in two-dimensional rectilinear ducts, subjected to suitable time-independent multi-dimensional boundary conditions…

Analysis of PDEs · Mathematics 2022-02-09 Junlei Gao , Hairong Yuan

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

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

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

In this paper, we prove the existence of two-dimensional solutions to the steady Euler-Poisson system with continuous transonic transitions across sonic interfaces of codimension 1. First, we establish the well-posedness of a boundary value…

Analysis of PDEs · Mathematics 2023-08-10 Myoungjean Bae , Ben Duan , Chunjing Xie

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