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We consider steady states of the incompressible Euler equation on two-dimensional domains. For non-radial analytic steady states on bounded simply connected domains, it was shown previously that there must be a global functional…

Analysis of PDEs · Mathematics 2026-05-12 Tarek M. Elgindi , Yupei Huang

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

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, 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

In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the…

Fluid Dynamics · Physics 2007-05-23 D. Iftimie , M. C. Lopes Filho , H. J. Nussenzveig Lopes

In this paper, we study the stability two-dimensional (2D) steady Euler flows with sharply concentrated vorticity in a simply-connected bounded domain. These flows are obtained as maximizers of the kinetic energy subject to the constraint…

Analysis of PDEs · Mathematics 2023-05-16 Guodong Wang

We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using the theory of integrable systems, any admissible…

Dynamical Systems · Mathematics 2022-04-07 Robert Cardona

We study the limiting behavior of the solutions of Euler equations of one-dimensional compressible fluid flow as the pressure like term vanishes. This system can be thought of as an approximation for the one dimensional model for large…

Analysis of PDEs · Mathematics 2018-03-06 Manas Ranjan Sahoo , Abhrojyoti Sen

Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…

Fluid Dynamics · Physics 2024-03-12 Jack S. Keeler , Mark G. Blyth

We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common…

Analysis of PDEs · Mathematics 2018-06-06 Fabio Pusateri , Klaus Widmayer

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

The motion of a compressible inviscid radiative flow can be described by the radiative Euler equations, which consists of the Euler system coupled with a Poisson equation for the radiative heat flux through the energy equation. Although…

Analysis of PDEs · Mathematics 2024-09-24 Huijiang Zhao , Boran Zhu

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, both smooth subsonic and transonic flows to steady Euler-Poisson system in a concentric cylinder are studied. We first establish the existence of cylindrically symmetric smooth subsonic and transonic flows to steady…

Analysis of PDEs · Mathematics 2023-08-23 Shangkun Weng , Wengang Yang , Na Zhang

We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…

Analysis of PDEs · Mathematics 2025-06-23 Alex Doak , Karsten Matthies , Jonathan Sewell , Miles H. Wheeler

This paper concerns the structural stability of smooth cylindrically symmetric supersonic spiral flows with large angular velocity for the steady Euler-Poisson system in a concentric cylinder. We establish the existence and uniqueness of…

Analysis of PDEs · Mathematics 2025-06-06 Chunpeng Wang , Zihao Zhang

The purpose of this work is to prove existence of a weak solution of the two dimensional incompressible Euler equations on a noncylindrical domain consisting of a smooth, bounded, connected and simply connected domain undergoing a…

Analysis of PDEs · Mathematics 2007-12-26 Flavia Z. Fernandes , Milton C. Lopes Filho

In this paper, we justify the low Mach number limit of the steady irrotational Euler flows for the airfoil problem, which is the first result for the low Mach number limit of the steady Euler flows in an exterior domain. The uniform…

Analysis of PDEs · Mathematics 2019-01-15 Mingjie Li , Tian-Yi Wang , Wei Xiang

Despite the physical importance, there are limited mathematical theories for the compressible Navier-Stokes equations with strong boundary layers. This is mainly due to the absence of a stream function structure, unlike the extensively…

Analysis of PDEs · Mathematics 2025-02-12 Shengxin Li , Tong Yang , Zhu Zhang

We consider solutions of the 2-d compressible Euler equations that are steady and self-similar. They arise naturally at interaction points in genuinely multi-dimensional flow. We characterize the possible solutions in the class of flows…

Analysis of PDEs · Mathematics 2012-11-14 Volker Elling , Joseph Roberts