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This paper concerns the study of the incompressible Euler equations with variable density, in the case of space dimension $d=2$. Contrarily to their homogeneous (constant density) counterpart, those equations are not known to be well-posed…

Analysis of PDEs · Mathematics 2025-02-17 Francesco Fanelli

An important physical model describing the dynamics of dilute weakly ionized plasmas in the collisional kinetic theory is the Vlasov-Poisson-Boltzmann system for which the plasma responds strongly to the self-consistent electrostatic force.…

Analysis of PDEs · Mathematics 2012-03-20 Renjun Duan , Tong Yang , Huijiang Zhao

We are interested in coupled semi-linear wave equations satisfying the null condition in two space dimensions, a basic model in nonlinear wave equations. Our aim is to establish global existence of smooth solutions to this system with large…

Analysis of PDEs · Mathematics 2025-07-21 Bingbing Ding , Shijie Dong , Gang Xu

The classical Euler--Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess…

Exactly Solvable and Integrable Systems · Physics 2015-06-15 Yuri N. Fedorov , Andrzej J. Maciejewski , Maria Przybylska

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

We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity…

Analysis of PDEs · Mathematics 2020-05-26 Helge Kristian Jenssen , Charis Tsikkou

Supersonic-sonic patches are ubiquitous in regions of transonic flows and they boil down to a family of degenerate hyperbolic problems in regions surrounded by a streamline, a characteristic curve and a possible sonic curve. This paper…

Analysis of PDEs · Mathematics 2019-04-12 Yanbo Hu , Jiequan Li

This paper is concerned with the large-time behavior of solutions to the Cauchy problem on the two-fluid Euler-Maxwell system with collisions when initial data are around a constant equilibrium state. The main goal is the rigorous…

Analysis of PDEs · Mathematics 2014-12-02 Renjun Duan , Qingqing Liu , Changjiang Zhu

We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…

Analysis of PDEs · Mathematics 2021-07-27 Huanyao Wen

We study the Klein-Gordon-Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the global existence of solutions and characterize their sharp…

Analysis of PDEs · Mathematics 2025-09-04 Shijie Dong , Zihua Guo , Kuijie Li

This paper focuses on the structure of classical sonic-supersonic solutions near sonic curves for the two-dimensional full Euler equations in gas dynamics. In order to deal with the parabolic degeneracy near the sonic curve, a novel set of…

Analysis of PDEs · Mathematics 2019-10-23 Yanbo Hu , Jiequan Li

We present a solver of 3D two-fluid plasma model for the simulation of short-pulse laser interactions with plasma. This solver resolves the equations of the two-fluid plasma model with ideal gas closure. We also include the…

Plasma Physics · Physics 2021-02-26 B. Morel , R. Giust , K. Ardaneh , F. Courvoisier

We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…

Analysis of PDEs · Mathematics 2016-07-04 Young-Pil Choi

In this paper, we consider the dispersive limit of the Euler-Poisson system for ion-acoustic waves. We establish that under the Gardner-Morikawa type transformations, the solutions of the Euler-Poisson system converge globally to the…

Mathematical Physics · Physics 2013-04-30 Xueke Pu

We prove that for the two-dimensional steady complete compressible Euler system, with given uniform upcoming supersonic flows, the following three fundamental flow patterns (special solutions) in gas dynamics involving transonic shocks are…

Analysis of PDEs · Mathematics 2010-04-13 Beixiang Fang , Li Liu , Hairong Yuan

This paper is concerned with the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar one (UEP) through the infinity-ion-mass limit by letting the ratio of the mass of ion $m_i$ over that of electron $m_e$ goes to…

Analysis of PDEs · Mathematics 2026-02-03 Yachun Li , Shihao Wang , Liang Zhao

In this paper, we are concerned with the structural stability of some steady subsonic solutions for Euler-Poisson system. A steady subsonic solution with subsonic background charge is proven to be structurally stable with respect to small…

Analysis of PDEs · Mathematics 2016-03-16 Shangkun Weng

A new Lagrangian particle method for solving Euler equations for compressible inviscid fluid or gas flows is proposed. Similar to smoothed particle hydrodynamics (SPH), the method represents fluid cells with Lagrangian particles and is…

Numerical Analysis · Mathematics 2016-03-21 Hsin-Chiang Chen , Roman Samulyak , Wei Li

The Euler-Poisson (EP) system models the dynamics of a variety of physical processes, including charge transport, collisional plasmas, and certain cosmological wave phenomena. In this work, we establish sharp critical threshold conditions…

Analysis of PDEs · Mathematics 2025-12-18 Manas Bhatnagar , Hailiang Liu

In this paper we propose a novel and general approach to design semi-implicit methods for the simulation of fluid-structure interaction problems in a fully Eulerian framework. In order to properly present the new method, we focus on the…

Numerical Analysis · Mathematics 2023-10-31 Mirco Ciallella , Thomas Milcent