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A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp corner, in a…

Soft Condensed Matter · Physics 2024-05-21 Francesco Dal Corso , Marco Amato , Davide Bigoni

In this paper, we establish two stability theorems for steady or traveling solutions of the two-dimensional incompressible Euler equation in a finite periodic channel, extending Arnold's classical work from the 1960s. Compared to Arnold's…

Analysis of PDEs · Mathematics 2025-04-08 Guodong Wang

The recently introduced structured input-output analysis is a powerful method for capturing nonlinear phenomena associated with incompressible flows, and this paper extends that method to the compressible regime. The proposed method relies…

Fluid Dynamics · Physics 2025-03-06 Diganta Bhattacharjee , Talha Mushtaq , Peter Seiler , Maziar S. Hemati

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 present an analysis of the stability, energy and torque properties of a model Bursian diode in a one dimensional Eulerian framework using the cold Euler-Poisson fluid equations. In regions of parameter space where there are two sets of…

Plasma Physics · Physics 2013-05-01 M. S. Rosin , H. Sun

We present some recent developments on shock capturing methods for nonlinear hyperbolic systems of balance laws, whose prototype is the Euler system of compressible fluid flows, and especially discuss {structure-preserving} techniques. The…

Analysis of PDEs · Mathematics 2015-12-29 Philippe G. LeFloch

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

In this paper, we consider the well-posedness theory of two-dimensional compressible subsonic jet flows for steady full Euler system with general vorticity. Inspired by the analysis in arXiv:2006.05672, we show that the stream function…

Analysis of PDEs · Mathematics 2024-04-26 Yan Li

A compactness framework is established for approximate solutions to subsonic-sonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional…

Analysis of PDEs · Mathematics 2015-07-28 Gui-Qiang G. Chen , Fei-Min Huang , Tian-Yi Wang

The unsteady response of nozzles with steady heat transfer forced by acoustic and/or entropy waves is modelled. The approach is based on the quasi-one-dimensional linearised Euler equations. The equations are cast in terms of three…

Fluid Dynamics · Physics 2022-03-02 Saikumar R. Yeddula , Juan Guzmán-Iñigo , Aimee S. Morgans

Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…

Analysis of PDEs · Mathematics 2021-03-31 Peter Constantin , Theodore D. Drivas , Daniel Ginsberg

The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…

Fluid Dynamics · Physics 2021-01-01 Marianna A. Shubov , Madeline M. Edwards

Incompressible Euler flows in narrow domains, in which the horizontal length scale is much larger than other scales, play an important role in applications, and their leading-order behavior can be described by the hydrostatic Euler…

Analysis of PDEs · Mathematics 2023-01-26 Wang Shing Leung , Tak Kwong Wong , Chunjing Xie

In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm…

Analysis of PDEs · Mathematics 2019-04-24 Corrado Lattanzio , Pierangelo Marcati , Delyan Zhelyazov

Base-flow computations and stability analyses are performed for a hypersonic wind tunnel nozzle at a Mach number of 6. Isothermal and adiabatic wall boundary conditions are investigated, and moderate stagnation conditions are used to…

In this paper, we study the initial-boundary value problem of compressible Euler equations with friction and heating that model the combined Fanno-Rayleigh flows through symmetric variable area nozzles, in particular, the case of…

Analysis of PDEs · Mathematics 2016-12-01 Shih-Wei Chou , John M. Hong , Bo-Chih Huang , Reyna Quita

We study the well-posedness of compressible vortex sheets and entropy waves in two-dimensional steady supersonic Euler flows over Lipschitz walls with $BV$ incoming flows. Both the Lipschitz wall of $BV$ tangential angle function and the…

Analysis of PDEs · Mathematics 2022-04-27 Gui-Qiang G. Chen , Vaibhav Kukreja

We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…

Analysis of PDEs · Mathematics 2024-08-30 Theodore D. Drivas , Tarek M. Elgindi , In-Jee Jeong

We derive a new formulation of the $3D$ compressible Euler equations with dynamic entropy exhibiting remarkable null structures and regularity properties. Our results hold for an arbitrary equation of state (which yields the pressure in…

Analysis of PDEs · Mathematics 2017-01-25 Jared Speck

Shock buffet on wings encountered in edge-of-the-envelope transonic flight remains an unresolved and disputed flow phenomenon, challenging both fundamental fluid mechanics and applied aircraft aerodynamics. The question of global…

Fluid Dynamics · Physics 2018-06-20 Sebastian Timme