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Related papers: Smooth Transonic Flows in De Laval Nozzles

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This paper concerns supersonic flows with nonzero vorticity governed by the steady Euler-Poisson system, under the coupled effects of the electric potential and the geometry of a convergent nozzle. By the coordinate rotation, the existence…

Analysis of PDEs · Mathematics 2026-05-01 Yuanyuan Xing , Zihao Zhang

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 prove the existence and stability of subsonic flows for steady full Euler-Poisson system in a two dimensional nozzle of finite length when imposing the electric potential difference on non-insulated boundary from a fixed…

Analysis of PDEs · Mathematics 2013-09-16 Myoungjean Bae , Ben Duan , Chunjing Xie

In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary…

Analysis of PDEs · Mathematics 2023-10-20 Na Zhang

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

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles without the assumption of irrotationality. It is shown that when the variation of Bernoulli's function in the upstream is…

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

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

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 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

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

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

The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong…

Analysis of PDEs · Mathematics 2018-01-10 Gui-Qiang G. Chen , Jun Chen , Mikhail Feldman

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 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

In this article, we prove the existence and regularity of a smooth solution for a supersonic-sonic patch arising in a modified Frankl problem in the study of three-dimensional axisymmetric steady isentropic relativistic transonic flows over…

Analysis of PDEs · Mathematics 2022-10-18 Rahul Barthwal , T. Raja Sekhar

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 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

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

This paper concerns the structural stability of smooth cylindrical symmetric transonic flows in a concentric cylinder under helically symmetric perturbation of suitable boundary conditions. The deformation-curl decomposition developed by…

Analysis of PDEs · Mathematics 2024-03-20 Yi Ke , Shangkun Weng