English
Related papers

Related papers: Global Uniqueness of Steady Transonic Shocks in Tw…

200 papers

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…

Analysis of PDEs · Mathematics 2015-06-11 Gui-Qiang Chen , Vaibhav Kukreja , Hairong Yuan

In this paper, we are trying to show the uniqueness of transonic shock solutions in an expanding nozzle under certain conditions and assumptions on the boundary data and the shock solution. The idea is to compare two transonic shock…

Analysis of PDEs · Mathematics 2025-02-11 Beixiang Fang , Xin Gao , 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 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

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 local uniqueness of steady transonic shock solutions with spherical symmetry for the three-dimensional full Euler equations. These transonic shock-fronts are important for understanding transonic shock phenomena in…

Analysis of PDEs · Mathematics 2011-12-09 Gui-Qiang G. Chen , Hairong Yuan

Transonic shocks play a pivotal role in designation of supersonic inlets and ramjets. For the three-dimensional steady non-isentropic compressible Euler system with frictions, we had constructed a family of transonic shock solutions in…

Analysis of PDEs · Mathematics 2018-11-21 Hairong Yuan , Qin Zhao

We study the uniqueness of solutions with a transonic shock in a duct in a class of transonic shock solutions, which are not necessarily small perturbations of the background solution, for steady potential flow. We prove that, for given…

Analysis of PDEs · Mathematics 2008-11-04 Gui-Qiang Chen , 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 are concerned with geometric properties of transonic shocks as free boundaries in two-dimensional self-similar coordinates for compressible fluid flows, which are not only important for the understanding of geometric structure and…

Analysis of PDEs · Mathematics 2020-06-09 Gui-Qiang G. Chen , Mikhail Feldman , Wei Xiang

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

In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to…

Analysis of PDEs · Mathematics 2015-05-19 Tao Luo , Jeffrey Rauch , 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

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 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

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

We establish existence, uniqueness and stability of transonic shocks for steady compressible non-isentropic potential flow system in a multidimensional divergent nozzle with an arbitrary smooth cross-section, for a prescribed exit pressure.…

Analysis of PDEs · Mathematics 2015-05-18 Myoungjean Bae , Mikhail Feldman

We study the uniqueness of solutions with a transonic shock in a two-dimensional Riemannian manifold with a special metric, which can be regarded as an approximate model of the general physical nozzles, within a class of transonic shock…

Analysis of PDEs · Mathematics 2025-09-01 Minghong Han , Bingsong Long , Hairong Yuan

For a class of external forces, we prove the existence and uniqueness of smooth transonic flows to the one dimensional steady Euler system with an external force, which is subsonic at the inlet and flows out at supersonic speed after…

Analysis of PDEs · Mathematics 2024-03-26 Shangkun Weng , Yan Zhou

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
‹ Prev 1 2 3 10 Next ›