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We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are…

Analysis of PDEs · Mathematics 2021-05-25 Gui-Qiang G. Chen , Jie Kuang , Yongqian Zhang

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

This paper concerns smooth transonic flows of Meyer type in finite de Laval nozzles, which are governed by an equation of mixed type with degeneracy and singularity at the sonic state. First we study the properties of sonic curves. For any…

Analysis of PDEs · Mathematics 2013-04-10 Chunpeng Wang , Zhouping Xin

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, we study the uniqueness of the steady 1-D shock solutions for the inviscid compressible Euler system in a finite nozzle via asymptotic analysis for physical parameters. The parameters for the heat conductivity and the…

Analysis of PDEs · Mathematics 2023-11-14 Beixiang Fang , Su Jiang , Piye Sun

When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational,…

Analysis of PDEs · Mathematics 2019-10-08 Gui-Qiang G. Chen , Mikhail Feldman , Wei Xiang

In this paper we prove existence, uniqueness and regularity of certain perturbed (subsonic--supersonic) transonic potential flows in a two-dimensional Riemannian manifold with "convergent-divergent" metric, which is an approximate model of…

Analysis of PDEs · Mathematics 2011-02-19 Hairong Yuan , Yue He

The stability of an irreversible singularity, such as a Riemann shock to the full Euler system, in the absence of any technical conditions on perturbations, remains a major open problem even within mono-dimensional framework. A natural…

Analysis of PDEs · Mathematics 2025-06-18 Saehoon Eo , Namhyun Eun , Moon-Jin Kang

This paper concerns the well-posedness of subsonic flows in a three-dimensional finitely long cylinder with arbitrary cross section. We establish the existence and uniqueness of subsonic flows in the Sobolev space by prescribing the normal…

Analysis of PDEs · Mathematics 2024-01-17 Shangkun Weng , Changkui Yao

In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value…

Analysis of PDEs · Mathematics 2018-04-16 Feimin Huang , Jie Kuang , Dehua Wang , Wei Xiang

In this paper, we are concerned with the instability problem of a 3-D transonic oblique shock wave for the steady supersonic flow past an infinitely long sharp wedge. The flow is assumed to be isentropic and irrotational. It was indicated…

Analysis of PDEs · Mathematics 2014-07-22 Li Liang , Xu Gang , Yin Huicheng

We are concerned with global steady subsonic flows through general infinitely long nozzles for the full Euler equations. The problem is formulated as a boundary value problem in the unbounded domain for a nonlinear elliptic equation of…

Analysis of PDEs · Mathematics 2012-04-10 Gui-Qiang Chen , Xuemei Deng , Wei Xiang

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 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

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by…

Analysis of PDEs · Mathematics 2023-08-08 Shangkun Weng , Zihao Zhang

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

Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…

Analysis of PDEs · Mathematics 2019-12-25 Vladimir Yushutin

This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…

Analysis of PDEs · Mathematics 2021-08-23 Beixiang Fang , Feimin Huang , Wei Xiang , Feng Xiao

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

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles which are periodic in $x_1$ direction with the period $L$. It is shown that when the variation of Bernoulli function at some given…

Analysis of PDEs · Mathematics 2011-02-01 Chao Chen , Chunjing Xie