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The well-posedness for the supersonic solutions of the Euler-Poisson system for hydrodynamical model in semiconductor devices and plasmas is studied in this paper. We first reformulate the Euler-Poisson system in the supersonic region into…

Analysis of PDEs · Mathematics 2019-01-11 Myoungjean Bae , Ben Duan , Jingjing Xiao , Chunjing Xie

We prove the unique existence of supersonic solutions of the Euler- Poisson system for potential flow in a three-dimensional rectangular cylinder when prescribing the velocity and the strength of electric field at the entrance. Overall, the…

Analysis of PDEs · Mathematics 2021-03-03 Myoungjean Bae , Hyangdong Park

Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global non-isentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the…

Analysis of PDEs · Mathematics 2020-03-24 Geng Lai

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

We address the structural stability of 3-D axisymmetric subsonic flows with nonzero swirl for the steady compressible Euler-Poisson system in a cylinder supplemented with non small boundary data. A special Helmholtz decomposition of the…

Analysis of PDEs · Mathematics 2016-05-09 Myoungjean Bae , Shangkun Weng

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

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

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 prove the existence of a subsonic axisymmetric weak solution $({\bf u},\rho,p)$ with ${\bf u}=u_x{\bf e}_x+u_r{\bf e}_r+u_\theta{\bf e}_{\theta}$ to steady Euler system in a three-dimensional infinitely long cylinder $\mathcal{N}$ when…

Analysis of PDEs · Mathematics 2019-04-19 Myoungjean Bae , Hyangdong Park

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 consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…

Analysis of PDEs · Mathematics 2007-05-23 J. Vanneste , D. Wirosoetisno

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

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 smooth supersonic flows with Lipschitz continuous speed in two-dimensional infinite expanding nozzles, which are governed by a quasilinear hyperbolic equation being singular at the sonic and vacuum state. The flow…

Analysis of PDEs · Mathematics 2014-10-16 Chunpeng Wang , Zhouping Xin

We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are…

Analysis of PDEs · Mathematics 2010-04-13 Beixiang Fang , Li Liu , Hairong Yuan

This paper is concerned with the study of the nonlinear stability of the contact discontinuity of the Navier-Stokes-Poisson system with free boundary in the case where the electron background density satisfies an analogue of the Boltzmann…

Analysis of PDEs · Mathematics 2015-08-07 Shuangqian Liu , Haiyan Yin , Changjiang Zhu

For a supersonic Euler flow past a straight wedge whose vertex angle is less than the extreme angle, there exists a shock-front emanating from the wedge vertex, and the shock-front is usually strong especially when the vertex angle of the…

Analysis of PDEs · Mathematics 2007-05-23 Gui-Qiang Chen , Tian-Hong Li

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

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…

Analysis of PDEs · Mathematics 2015-07-28 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang

Given constant data of density $\rho_0$, velocity $-u_0{\bf e}_r$, pressure $p_0$ and electric force $-E_0{\bf e}_r$ for supersonic flow at the entrance, and constant pressure $p_{\rm ex}$ for subsonic flow at the exit, we prove that…

Analysis of PDEs · Mathematics 2017-03-01 Myoungjean Bae , Yong Park