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Related papers: Supersonic flow past an airfoil

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This paper concerns supersonic flows with nonzero vorticity governed by the steady Euler-Poisson system, under the coupled effects of the electric potential and the geometry of a convergent nozzle. By the coordinate rotation, the existence…

Analysis of PDEs · Mathematics 2026-05-01 Yuanyuan Xing , Zihao Zhang

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

We construct a supersonic-sonic smooth patch solution for the two dimensional steady Euler equations in gas dynamics. This patch is extracted from the Frankl problem in the study of transonic flow with local supersonic bubble over an…

Analysis of PDEs · Mathematics 2021-01-05 Yanbo Hu , Jiequan Li

We consider the classical compressible Euler's Equations in three space dimensions with an arbitrary equation of state, and whose initial data corresponds to a constant state outside a sphere. Under suitable restriction on the size of the…

Analysis of PDEs · Mathematics 2013-05-07 Demetrios Christodoulou , Shuang Miao

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

Supersonic flows for the two-dimensional (2D) steady full Euler system are studied. We construct a global non-isentropic rotational supersonic flow in a semi-infinite divergent duct. The flow satisfies the slip condition on the walls of the…

Analysis of PDEs · Mathematics 2020-03-24 Geng Lai

We develop a method that works in general product Riemannian manifold to decompose the three-dimensional steady full compressible Euler system, which is of elliptic-hyperbolic composite-mixed type for subsonic flows. The method is applied…

Analysis of PDEs · Mathematics 2015-05-13 Li Liu , Gang Xu , Hairong Yuan

This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of [7,11,15,20]. The maximum principle is applied to estimate the potential…

Analysis of PDEs · Mathematics 2023-04-10 Lei Ma , Tian-Yi Wang

The dynamics along the particle trajectories for the 3D axisymmetric Euler equations are considered. It is shown that if the inflow is rapidly increasing (pushy) in time, the corresponding laminar profile of the incompressible Euler flow is…

Analysis of PDEs · Mathematics 2017-05-15 Tsuyoshi Yoneda

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 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

In this article, we prove the existence and regularity of a smooth solution for a supersonic-sonic patch arising in a modified Frankl problem in the study of three-dimensional axisymmetric steady isentropic relativistic transonic flows over…

Analysis of PDEs · Mathematics 2022-10-18 Rahul Barthwal , T. Raja Sekhar

We present our recent results on the Prandtl-Meyer reflection for supersonic potential flow past a solid ramp. When a steady supersonic flow passes a solid ramp, there are two possible configurations: the weak shock solution and the strong…

Analysis of PDEs · Mathematics 2012-01-04 Myoungjean Bae , Gui-Qiang Chen , Mikhail Feldman

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 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

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

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

The existence, uniqueness, and asymptotic behavior of steady transonic flows past a curved wedge, involving transonic shocks, governed by the two-dimensional full Euler equations are established. The stability of both weak and strong…

Analysis of PDEs · Mathematics 2018-01-10 Gui-Qiang G. Chen , Jun Chen , Mikhail Feldman

The dynamics along the particle trajectories for the 3D axisymmetric Euler equations in an infinite cylinder are considered. It is shown that if the inflow-outflow is rapidly increasing in time, the corresponding laminar profile of the…

Analysis of PDEs · Mathematics 2016-10-31 Tsuyoshi Yoneda

Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…

Mathematical Physics · Physics 2020-04-13 Valentin Lychagin , Mikhail Roop