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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 consider a supersonic flow past an airfoil in the context of the steady, isentropic and irrotational compressible Euler equations. We show that for appropriate data, either a shock forms, in which case certain derivatives of the solution…

Analysis of PDEs · Mathematics 2024-01-05 Yannis Angelopoulos

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 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

This paper concerns studies on smooth transonic flows with nonzero vorticity in De Laval nozzles for a quasi two dimensional steady Euler flow model which is a generalization of the classical quasi one dimensional model. First, the…

Analysis of PDEs · Mathematics 2024-05-29 Shangkun Weng , Zhouping Xin

We analyze rarefaction wave interactions of self-similar transonic irrotational flow in gas dynamics for the two dimensional Riemann problems. We establish the existence result of the supersonic solution to the prototype nonlinear wave…

Analysis of PDEs · Mathematics 2017-09-05 Eun Heui Kim , Charis Tsikkou

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

Turbine blades operating in transonic-supersonic regime develop a complex shock wave system at the trailing edge, a phenomenon that leads to unfavorable pressure perturbations downstream and can interact with other turbine stages.…

Fluid Dynamics · Physics 2019-01-10 Alejandro Martinez-Cava , Yinzhu Wang , Javier de Vicente , Eusebio Valero

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 investigate the qualitative dynamics of smooth solutions to the radially symmetric isentropic compressible Euler equations, focusing specifically on the evolution of rarefactive and compressive wave characters across three distinct…

Analysis of PDEs · Mathematics 2026-03-11 Eduardo Abreu , Geng Chen , Faris El-Katri , Erivaldo Lima

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

In the paper we are concerned with the large time behavior of solutions to the one-dimensional Navier-Stokes-Poisson system in the case when the potential function of the self-consistent electric field may take distinct constant states at…

Analysis of PDEs · Mathematics 2014-12-31 Renjun Duan , Shuangqian Liu

We consider the complete Euler system describing the time evolution of an inviscid non-isothermal gas. We show that the rarefaction wave solutions of the 1D Riemann problem are stable, in particular unique, in the class of all bounded weak…

Analysis of PDEs · Mathematics 2014-12-08 Eduard Feireisl , Ondřej Kreml , Alexis Vasseur

The inflow problem of full compressible Navier-Stokes equations is considered on the half line $(0,+\infty)$. Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state…

Analysis of PDEs · Mathematics 2009-03-25 Xiaohong Qin , Yi Wang

In this paper, we prove the existence and uniqueness of subsonic solutions to the steady Euler flows past a smooth, axisymmetric obstacle. Specifically, for a broad class of prescribed positive axial velocities in the upstream, the subsonic…

Analysis of PDEs · Mathematics 2026-02-27 Dehua Wang , Tian-Yi Wang , Weiqiang Wang

This paper is concerned with the study of nonlinear stability of superposition of boundary layer and rarefaction wave on the two-fluid Navier-Stokes-Poisson system in the half line $\mathbb{R}_{+}=:(0,+\infty)$. On account of the…

Analysis of PDEs · Mathematics 2015-08-07 Haiyan Yin , Jinshun Zhang , Changjiang Zhu

In this paper, we establish the existence of three-dimensional axisymmetric compressible jet flows for steady Euler system with large vorticity by using the variational method. More precisely, for given axial velocity of the flow at the…

Analysis of PDEs · Mathematics 2024-05-20 Yan Li

We establish unique existence and stability of subsonic potential flow for steady Euler-Poisson system in a multidimensional nozzle of a finite length when prescribing the electric potential difference on non-insulated boundary from a fixed…

Analysis of PDEs · Mathematics 2013-06-04 Myoungjean Bae , Ben Duan , Chunjing Xie

Within the transonic regime, the aeroelastic problems exhibit many unique characteristics compared with subsonic and supersonic cases. Although a lot of research has been carried out in this field, the underlying mechanisms of these complex…

Fluid Dynamics · Physics 2020-02-11 Chuanqiang Gao , Weiwei 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