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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

Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…

Fluid Dynamics · Physics 2024-03-12 Jack S. Keeler , Mark G. Blyth

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

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, 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

In this paper, we investigate steady inviscid compressible flows with radial symmetry in an annulus. The major concerns are transonic flows with or without shocks. One of the main motivations is to elucidate the role played by the angular…

Analysis of PDEs · Mathematics 2021-01-05 Shangkun Weng , Zhouping Xin , Hongwei Yuan

In this paper, a compensated compactness framework is established for sonic-subsonic approximate solutions to the $n$-dimensional$(n\geq 2)$ Euler equations for steady irrotational flow that may contain stagnation points. This compactness…

Analysis of PDEs · Mathematics 2015-03-19 Feimin Huang , Tianyi Wang , Yong Wang

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

Studies on singular flows in which either the velocity fields or the vorticity fields change dramatically on small regions are of considerable interests in both the mathematical theory and applications. Important examples of such flows…

Analysis of PDEs · Mathematics 2007-05-23 Zhouping Xin

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 structurally nonlinear stability of supersonic contact discontinuities in three-dimensional compressible isentropic steady flows. Based on the weakly linear stability result and the $L^2$-estimates obtained by…

Analysis of PDEs · Mathematics 2014-07-08 Ya-Guang Wang , Fang Yu

We establish the existence and stability of the transonic shock solution to three-dimensional axisymmetric Euler system with an external force in a cylinder under perturbations of the incoming supersonic flow, the exit pressure, the…

Analysis of PDEs · Mathematics 2026-05-26 Zihao Zhang

We demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this…

Analysis of PDEs · Mathematics 2025-01-28 Xiaomin Zhang , Peng Qu , Huimin Yu

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…

Analysis of PDEs · Mathematics 2019-02-19 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang , Wei Xiang

We study the well-posedness of compressible vortex sheets and entropy waves in two-dimensional steady supersonic Euler flows over Lipschitz walls with $BV$ incoming flows. Both the Lipschitz wall of $BV$ tangential angle function and the…

Analysis of PDEs · Mathematics 2022-04-27 Gui-Qiang G. Chen , Vaibhav Kukreja

We study the two-dimensional incompressible Navier-Stokes equations in a channel $\Omega=(0,L)\times(0,H)$ with small viscosity $\varepsilon\ll1$, an $\varepsilon$-Navier slip condition on the horizontal walls, and a viscous inflow…

Analysis of PDEs · Mathematics 2026-02-24 Yan Guo , Zhuolun Yang

This paper concerns the well-posedness of subsonic Euler-Poisson flows in a convergent nozzle. Due to the geometry of the nozzle, we first introduce a coordinate transformation to prove the existence of radially symmetric subsonic solutions…

Analysis of PDEs · Mathematics 2026-04-28 Yuanyuan Xing , Zihao Zhang

Control surface deployment in a supersonic flow has many applications, including flow control, mixing, and body-force regulation. The extent of control surface deflections introduces varying flow unsteadiness. The resulting fluid dynamics…

Fluid Dynamics · Physics 2022-10-26 S. K. Karthick , D. Bhelave , A. De

We study supersonic flow past a convex corner which is surrounded by quiescent gas. When the pressure of the upstream supersonic flow is larger than that of the quiescent gas, there appears a strong rarefaction wave to rarefy the supersonic…

Analysis of PDEs · Mathematics 2018-01-16 Min Ding , Hairong Yuan

We formulated a problem on hypersonic limit of two-dimensional steady non-isentropic compressible Euler flows passing a straight wedge. It turns out that Mach number of the upcoming uniform supersonic flow increases to infinite may be taken…

Analysis of PDEs · Mathematics 2019-04-09 Aifang Qu , Hairong Yuan , Qin Zhao