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We are concerned with the stability of multidimensional (M-D) transonic shocks in steady supersonic flow past multidimensional wedges. One of our motivations is that the global stability issue for the M-D case is much more sensitive than…

Analysis of PDEs · Mathematics 2017-05-23 Gui-Qiang Chen , Beixiang Fang

This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…

Analysis of PDEs · Mathematics 2021-08-23 Beixiang Fang , Feimin Huang , Wei Xiang , Feng Xiao

Theoretical studies of transonic accretion onto black holes reveal a wide range of possible solutions, broadly classified into smooth flows and flows featuring shocks. Accretion solutions that involve the formation of shocks are…

High Energy Astrophysical Phenomena · Physics 2025-12-16 Raj Kishor Joshi , Antonios Tsokaros , Sanjit Debnath , Indranil Chattopadhyay , Ramiz Aktar

In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary…

Analysis of PDEs · Mathematics 2023-10-20 Na Zhang

We consider the problem of supersonic flow of a Chaplygin gas past a delta wing with a shock or rarefaction wave attached to the leading edges. The flow under study is described by the three-dimensional steady Euler system. In conical…

Analysis of PDEs · Mathematics 2020-12-29 Bingsong Long , Chao Yi

An analytical solution for high supersonic flow over a circular cylinder based on Schneider's inverse method has been presented. In the inverse method, a shock shape is assumed and the corresponding flow field and the shape of the body…

Numerical Analysis · Mathematics 2023-08-01 S R Siva Prasad Kochi , M Ramakrishna

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 demonstrate that it is possible to control a normal transonic shock to move periodically by adjusting the boundary conditions at the entrance or the exit of the tube, for which, the phenomena has been observed in engineering. In this…

Analysis of PDEs · Mathematics 2025-01-28 Xiaomin Zhang , Peng Qu , Huimin Yu

It has recently been shown that the maximal kinematical invariance group of polytropic fluids, for smooth subsonic flows, is the semidirect product of SL(2,R) and the static Galilei group G. This result purports to offer a theoretical…

Mathematical Physics · Physics 2009-11-10 Oliver Jahn , V. V. Sreedhar , Amitabh Virmani

Guderley's 1942 work on radial shock waves provides cases of self-similar Euler flows exhibiting blowup of primary (undifferentiated) flow variables: a converging shock wave invades a quiescent region, and the velocity and pressure in its…

Fluid Dynamics · Physics 2023-01-23 Helge Kristian Jenssen , Charis Tsikkou

The classical problem of the flow over a circular cylinder at Reynolds number 40 is considered using an accurate pseudo-spectral code. A new set of boundary conditions is proposed to improve the representation of the infinite flow domain,…

Fluid Dynamics · Physics 2013-10-25 Rémi Gautier , Damien Biau , Eric Lamballais

We present a rigorous approach and related techniques to construct global solutions of the 2-D Riemann problem with four-shock interactions for the Euler equations for potential flow. With the introduction of three critical angles: the…

Analysis of PDEs · Mathematics 2023-05-25 Gui-Qiang G. Chen , Alexander Cliffe , Feimin Huang , Song Liu , Qin Wang

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

Shock waves are fundamental in nature. One of the most fundamental problems in fluid mechanics is shock reflection-diffraction by wedges. The complexity of reflection-diffraction configurations was first reported by Ernst Mach in 1878. The…

Analysis of PDEs · Mathematics 2013-11-25 Gui-Qiang G. Chen , Mikhail Feldman

We consider the problem of 2D supersonic flow onto a solid wedge, or equivalently in a concave corner formed by two solid walls. For mild corners, there are two possible steady state solutions, one with a strong and one with a weak shock…

Mathematical Physics · Physics 2009-09-29 Volker Elling , Tai-Ping Liu

A new type of self-similarity is found in the problem of a plane-parallel, ultra-relativistic blast wave, propagating in a powerlaw density profile of the form $\rho \propto z^{-k}$. Self-similar solutions of the first kind can be found for…

High Energy Astrophysical Phenomena · Physics 2024-02-14 Tamar Faran , Andrei Gruzinov , Re'em Sari

The study of fluids has been a topic of intense research for several hundred years. Over the years, this has further increased due to improved computational facility, which makes it easy to numerically simulate the fluid dynamics, which was…

Fluid Dynamics · Physics 2021-03-05 Soumen Roy

This paper proposes a simple new closure principle for turbulent shear flows. The turbulent flow field is divided into an outer and an inner region. The inner region is made up of a log-law region and a wall layer. The wall layer is viewed…

Fluid Dynamics · Physics 2010-01-15 Trinh Khanh Tuoc

This paper concerns the well-posedness of subsonic flows in a three-dimensional finitely long cylinder with arbitrary cross section. We establish the existence and uniqueness of subsonic flows in the Sobolev space by prescribing the normal…

Analysis of PDEs · Mathematics 2024-01-17 Shangkun Weng , Changkui Yao

In this paper, we study the global existence of steady subsonic Euler flows through infinitely long nozzles without the assumption of irrotationality. It is shown that when the variation of Bernoulli's function in the upstream is…

Analysis of PDEs · Mathematics 2009-07-21 Chunjing Xie , Zhouping Xin