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In this paper, uniqueness and uniform structural stability of Poiseuille flows in an infinitely long pipe with Navier boundary conditions are established for axisymmetric solutions of steady Navier-Stokes system. The crucial point is that…

Analysis of PDEs · Mathematics 2021-11-18 Yun Wang , Chunjing Xie

This paper concerns studies on smooth transonic flows with nonzero vorticity in De Laval nozzles for a quasi two dimensional steady Euler flow model which is a generalization of the classical quasi one dimensional model. First, the…

Analysis of PDEs · Mathematics 2024-05-29 Shangkun Weng , Zhouping Xin

In this work, we study convection-diffusion equations in the cases of bounded drifts and drifts induced by the gradient of a potential. We define a new notion of solution and prove its existence and uniqueness. Furthermore, we show the…

Analysis of PDEs · Mathematics 2023-11-10 Alireza Ataei

Turbine blades operating in transonic-supersonic regime develop a complex shock wave system at the trailing edge, a phenomenon that leads to unfavorable pressure perturbations downstream and can interact with other turbine stages.…

Fluid Dynamics · Physics 2019-01-10 Alejandro Martinez-Cava , Yinzhu Wang , Javier de Vicente , Eusebio Valero

We consider a particular instance of reflection of shock waves in self-similar compressible flow. We prove that local self-similar regular reflection (RR) cannot always be extended into a global flow. Therefore the detachment criterion is…

Mathematical Physics · Physics 2009-08-04 Volker Elling

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

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

The steady-state solution of fluid flow in pipeline infrastructure networks driven by junction/node potentials is a crucial ingredient in various decision-support tools for system design and operation. While the nonlinear system is known to…

Numerical Analysis · Mathematics 2024-10-23 Shriram Srinivasan , Nishant Panda , Kaarthik Sundar

The subject of this work is the shock development problem in fluid mechanics. A shock originates from an acoustically spacelike surface in spacetime at which the 1st derivatives of the physical variables blow up. The solution requires the…

Analysis of PDEs · Mathematics 2017-05-03 Demetrios Christodoulou

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

Two-dimensional steady supersonic ramp flows are important and well-studied flow patterns in aerodynamics. Vimercati, Kluwick and Guardone [J. Fluid Mech., 885 (2018) 445--468] constructed various self-similar composite wave solutions to…

Analysis of PDEs · Mathematics 2025-09-11 Geng Lai

This paper concerns the structural stability of smooth cylindrically symmetric supersonic Euler-Poisson flows in nozzles. Both three-dimensional and axisymmetric perturbations are considered. On one hand, we establish the existence and…

Analysis of PDEs · Mathematics 2025-03-21 Chunpeng Wang , Zihao Zhang

In this paper, we prove the local uniqueness of an inverse problem arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The direct problem is an initial-boundary…

Analysis of PDEs · Mathematics 2014-12-17 Aníbal Coronel , Marko Rojas-Medar

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

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

The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the 'bypass' path…

Fluid Dynamics · Physics 2010-07-02 Damien Biau , Houssam Soueid , Alessandro Bottaro

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

In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which…

Analysis of PDEs · Mathematics 2015-04-07 Jiaqing Pan

In this short note we present an instability result for transonic flows with respect to perturbations of the Mach number at infinity. More specifically we show that a perturbation of a transonic solution in the context of a Cauchy problem…

Analysis of PDEs · Mathematics 2021-09-29 Yannis Angelopoulos

This study is concerned with numerical linear stability analysis of liquid metal flow in a square duct with thin electrically conducting walls subject to a uniform transverse magnetic field. We derive an asymptotic solution for the base…

Fluid Dynamics · Physics 2016-01-27 Jānis Priede , Thomas Arlt , Leo Bühler
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