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In this paper, we proved the well-posedness theory of compressible subsonic jet flows for two-dimensional steady Euler system with {\it general} incoming horizontal velocity as long as the flux is larger than a critical value. One of the…

Analysis of PDEs · Mathematics 2024-02-23 Yan Li , Wenhui Shi , Lan Tang , Chunjing Xie

We establish the existence of an axisymmetric weak solution to the steady Euler system with a transonic shock, nonzero vorticity, and nonzero swirl in a three-dimensional cylinder. When prescribing the supersonic solution in the upstream…

Analysis of PDEs · Mathematics 2020-11-30 Hyangdong Park , Hyeongyu Ryu

We are concerned with the well-posedness of an inverse problem for determining the wedge boundary and associated two-dimensional steady supersonic Euler flow past the wedge, provided that the pressure distribution on the boundary surface of…

Analysis of PDEs · Mathematics 2024-09-30 Gui-Qiang G. Chen , Yun Pu , Yongqian Zhang

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 the structural stability of the transonic shocks for three dimensional axisymmetric Euler system with swirl velocity under the perturbations for the incoming supersonic flow, the nozzle boundary, and the exit…

Analysis of PDEs · Mathematics 2020-02-14 Shangkun Weng , Chunjing Xie , Zhouping Xin

In this work we systematically derive the governing equations of supersonic conical flow by projecting the 3D Euler equations onto the unit sphere. These equations result from taking the assumption of conical invariance on the 3D flow…

Analysis of PDEs · Mathematics 2019-10-22 Ian Holloway , Sivaguru S. Sritharan

In this paper, we prove the unique existence of three-dimensional supersonic solutions to the steady Euler-Poisson system in cylindrical nozzles when prescribing the velocity, entropy, and the strength of electric field at the entrance. We…

Analysis of PDEs · Mathematics 2024-03-08 Myoungjean Bae , Hyangdong Park

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 the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed…

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

We consider self-similar solutions to the full compressible Euler system for an ideal gas in two and three space dimensions. The system admits a 2-parameter family of similarity solutions depending on parameters $\lambda$ and $\kappa$.…

Analysis of PDEs · Mathematics 2022-06-01 Helge Kristian Jenssen , Alexander Anthony Johnson

For an upstream supersonic flow past a straight-sided cone in $\R^3$ whose vertex angle is less than the critical angle, a transonic (supersonic-subsonic) shock-front attached to the cone vertex can be formed in the flow. In this paper we…

Analysis of PDEs · Mathematics 2016-03-15 Gui-Qiang Chen , Beixiang Fang

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

This paper is devoted to the well-posedness theory of piston problem for compressible {combustion} Euler flows with physical ignition condition. A significant combustion phenomena called detonation will occur provided the reactant is…

Analysis of PDEs · Mathematics 2022-03-04 Kai Hu , Jie Kuang

We study the subsonic flows governed by full Euler equations in the half plane bounded below by a piecewise smooth curve asymptotically approaching x1-axis. Nonconstant conditions in the far field are prescribed to ensure the real Euler…

Analysis of PDEs · Mathematics 2007-10-22 Jun chen

In this paper, we are concerned with the structural stability of some steady subsonic solutions for Euler-Poisson system. A steady subsonic solution with subsonic background charge is proven to be structurally stable with respect to small…

Analysis of PDEs · Mathematics 2016-03-16 Shangkun Weng

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

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

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

The shock reflection problem is one of the most important problems in mathematical fluid dynamics, since this problem not only arises in many important physical situations but also is fundamental for the theory of multidimensional…

Analysis of PDEs · Mathematics 2015-05-13 Myoungjean Bae , Gui-Qiang Chen , Mikhail Feldman

In this paper, we first investigate the mathematical aspects of supersonic flow of a Chaplygin gas past a conical wing with diamond-shaped cross sections in the case of a shock wave detached from the leading edges. The flow under…

Analysis of PDEs · Mathematics 2026-01-16 Bingsong Long