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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 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 class of three-dimensional initial data characterized by uniformly large vorticity is considered for the Euler equations of incompressible fluids. The fast singular oscillating limits of the Euler equations are studied for parametrically…

Analysis of PDEs · Mathematics 2012-07-27 François Golse , Alex Mahalov , Basil Nicolaenko

In our previous work, we have established the existence of transonic characteristic discontinuities separating supersonic flows from a static gas in two-dimensional steady compressible Euler flows under a perturbation with small total…

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

This paper concerns the structural stability of supersonic flows with a contact discontinuity in a finitely long curved nozzle for the two-dimensional steady compressible rotating Euler system. Concerning the effect of Coriolis force, we…

Analysis of PDEs · Mathematics 2023-07-04 Shangkun Weng , Zihao Zhang

We establish the existence and stability of cylindrical transonic shock solutions under three dimensional perturbations of the incoming flows and the exit pressure without any further restrictions on the background transonic shock…

Analysis of PDEs · Mathematics 2024-01-23 Shangkun Weng , Zhouping Xin

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 establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely…

Analysis of PDEs · Mathematics 2019-02-19 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang , Wei Xiang

We establish the existence and uniqueness of some smooth accelerating transonic flows governed by the three dimensional steady compressible Euler equations with an external force in cylinders with arbitrary cross sections, which include…

Analysis of PDEs · Mathematics 2024-11-08 Shangkun Weng , Zhouping Xin

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

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

We prove a series of results tied to the regularity and geometry of solutions to the $3D$ compressible Euler equations with vorticity and entropy. Our framework exploits and reveals additional virtues of a recent new formulation of the…

Analysis of PDEs · Mathematics 2022-09-08 Marcelo M. Disconzi , Chenyun Luo , Giusy Mazzone , Jared Speck

In this paper, we are concerned with the global existence and stability of a smooth supersonic flow with vacuum state at infinity in a 3-D infinitely long divergent nozzle. The flow is described by a 3-D steady potential equation, which is…

Analysis of PDEs · Mathematics 2015-10-28 Xu Gang , Yin Huicheng

In this paper, we show that for given Bernoulli function and entropy function at the upstream, if the incoming mass flux is within a suitable range, then there exists a unique outer pressure such that smooth subsonic three-dimensional…

Analysis of PDEs · Mathematics 2024-05-13 Yan Li

We prove the stability of three-dimensional axisymmetric solutions to the steady Euler system with transonic shocks in divergent nozzles under perturbations of the exit pressure and the supersonic solution in the upstream region. We first…

Analysis of PDEs · Mathematics 2024-07-30 Hyangdong Park

In this paper, the well-posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established. More precisely, the global existence and…

Analysis of PDEs · Mathematics 2020-08-26 Lei Ma , Chunjing Xie

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

This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves for the two-dimensional full Euler equations in gas dynamics. In order to deal with the parabolic degeneracy near the sonic curve, a novel set of…

Analysis of PDEs · Mathematics 2019-10-23 Yanbo Hu , Jiequan Li

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

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