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This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak…

Analysis of PDEs · Mathematics 2026-03-26 Kotaro Horimoto

For a two-dimensional steady supersonic Euler flow past a convex cornered wall with right angle, a characteristic discontinuity (vortex sheet and/or entropy wave) is generated, which separates the supersonic flow from the gas at rest (hence…

Analysis of PDEs · Mathematics 2015-06-11 Gui-Qiang G. Chen , Vaibhav Kukreja , Hairong Yuan

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

We are concerned with the stability of steady multi-wave configurations for the full Euler equations of compressible fluid flow. In this paper, we focus on the stability of steady four-wave configurations that are the solutions of the…

Analysis of PDEs · Mathematics 2018-07-19 Gui-Qiang G. Chen , Matthew Rigby

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

In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible…

Analysis of PDEs · Mathematics 2024-08-09 Hai-Liang Li , Ling-Yun Shou

This is the first of a series of papers devoted to the initial value problem for the Euler system of compressible fluids and augmented versions containing higher-order terms. We encompass solutions that have finite total energy and enjoy a…

Analysis of PDEs · Mathematics 2012-12-24 Pierre Germain , Philippe G. LeFloch

We consider the Cauchy problem for the isentropic compressible Euler-Maxwell equations under general pressure laws in a three-dimensional periodic domain. For any smooth initial electron density away from the vacuum and smooth…

Analysis of PDEs · Mathematics 2023-05-23 Shunkai Mao , Peng Qu

We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…

Analysis of PDEs · Mathematics 2021-07-27 Huanyao Wen

We study the Cauchy problem of a $3\times 3$ system of conservation laws modeling two--phase flow of polymer flooding in rough porous media with possibly discontinuous permeability function. The system loses strict hyperbolicity in some…

Analysis of PDEs · Mathematics 2021-01-19 Graziano Guerra , Wen Shen

In this paper, we establish the existence and uniqueness of subsonic flows with a contact discontinuity in a two-dimensional finitely long slightly curved nozzle by prescribing the entropy, the Bernoulli's quantity and the horizontal mass…

Analysis of PDEs · Mathematics 2024-04-08 Shangkun Weng , Zihao Zhang

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

We investigate two dimensional steady Euler-Poisson system which describe the motion of compressible self-gravitating flows. The unique existence and stability of subsonic flows in a duct of finite length are obtained when prescribing the…

Analysis of PDEs · Mathematics 2014-06-18 Myoungjean Bae , Ben Duan , Chunjing Xie

The aim of this article is to study the limiting behavior of the solutions for the scaled generalized Euler equations of compressible fluid flow. When the initial data is of Riemann type, we showed the existence of solution which consists…

Analysis of PDEs · Mathematics 2019-07-17 Manas Ranjan Sahoo , Abhrojyoti Sen

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

Radial similarity flow offers a rare instance where concrete inviscid, multi-dimensional, compressible flows can be studied in detail. In particular, there are flows of this type that exhibit imploding shocks and cavities. In such flows the…

Analysis of PDEs · Mathematics 2019-01-01 Helge Kristian Jenssen , Charis Tsikkou

In this paper, we study the existence and uniqueness of three dimensional steady Euler flows in rectangular nozzles when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the…

Analysis of PDEs · Mathematics 2013-05-13 Chao Chen , Chunjing Xie

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

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

In this paper we developed an analysis of the compressible, isentropic Euler equations in two spatial dimensions for a generalized polytropic gas law. The main focus is rotational flows in the subsonic regimes, described through the…

Analysis of PDEs · Mathematics 2026-04-02 Talita Mello , Wladimir Neves