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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 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

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

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 develop a method that works in general product Riemannian manifold to decompose the three-dimensional steady full compressible Euler system, which is of elliptic-hyperbolic composite-mixed type for subsonic flows. The method is applied…

Analysis of PDEs · Mathematics 2015-05-13 Li Liu , Gang Xu , Hairong Yuan

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

This paper concerns the structural stability of smooth cylindrically symmetric supersonic spiral flows with large angular velocity for the steady Euler-Poisson system in a concentric cylinder. We establish the existence and uniqueness of…

Analysis of PDEs · Mathematics 2025-06-06 Chunpeng Wang , Zihao Zhang

We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than…

Analysis of PDEs · Mathematics 2017-05-23 Gui-Qiang Chen , Beixiang Fang

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 develop a new approach and employ it to establish the global existence and nonlinear structural stability of attached weak transonic shocks in steady potential flow past three-dimensional wedges; in particular, the restriction that the…

Analysis of PDEs · Mathematics 2021-08-10 Gui-Qiang G. Chen , Jun Chen , Wei Xiang

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

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

We prove the global uniqueness of multidimensional subsonic flows for the steady Euler--Poisson system in a bounded nozzle in the sense that uniqueness holds without restricting solutions to be small perturbations of a background state. The…

Analysis of PDEs · Mathematics 2026-04-28 Myoungjean Bae , Ben Duan , Chunjing Xie

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

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, 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

We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…

Analysis of PDEs · Mathematics 2024-11-08 Shangkun Weng , Zhouping Xin

For the stationary hydrodynamic model for semiconductors with sonic boundary, represented by Euler-Poisson equations, it possesses the various physical solutions including interior subsonic solutions/interior supersonic solutions/shock…

Analysis of PDEs · Mathematics 2022-04-05 Yue-Hong Feng , Haifeng Hu , Ming Mei

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

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