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In the present paper, we consider the initial value problem for the bipolar Vlasov-Poisson-Boltzmann (bVPB) system and its corresponding modified Vlasov-Poisson-Boltzmann (mVPB). We give the spectrum analysis on the linearized bVPB and mVPB…

Analysis of PDEs · Mathematics 2014-11-21 Hai-Liang Li , Tong Yang , Mingying Zhong

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 are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main…

Analysis of PDEs · Mathematics 2023-11-14 Gui-Qiang G. Chen , Lin He , Yong Wang , Difan Yuan

In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…

Analysis of PDEs · Mathematics 2026-05-19 Yong Wang , Hang Xiong , Hongyao Zhang

Using recent developments in the theory of globally defined expanding compressible gases, we construct a class of global-in-time solutions to the compressible 3-D Euler-Poisson system without any symmetry assumptions in both the…

Analysis of PDEs · Mathematics 2017-12-04 Mahir Hadzic , Juhi Jang

We justify the global-in-time validity of Hilbert expansion for the ionic Vlasov-Poisson-Boltzmann system in $\mathbb{R}^3$, a fundamental model describing ion dynamics in dilute collisional plasmas. As the Knudsen number approaches zero,…

Analysis of PDEs · Mathematics 2026-01-06 Fucai Li , Yichun Wang

We consider the Cauchy problem for a damped Euler-Maxwell system with no ionic background. For smooth enough data satisfying suitable so-called dispersive conditions, we establish the global in time existence and uniqueness of a strong…

Analysis of PDEs · Mathematics 2024-02-02 Bernard Ducomet , Šárka Nečasová , John Sebastian H. Simon

The Euler-Poisson(EP) system describes the dynamic behavior of many important physical flows. In this work, a Riccati system that governs the flow's gradient is studied. The evolution of divergence is governed by the Riccati type equation…

Analysis of PDEs · Mathematics 2020-07-17 Yongki Lee

In the present paper, we study the diffusion limit of the classical solution to the unipolar Vlasov-Poisson-Boltzmann (VPB) system with initial data near a global Maxwellian. We prove the convergence and establish the convergence rate of…

Analysis of PDEs · Mathematics 2021-06-09 Hai-Liang Li , Tong Yang , Mingying Zhong

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

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…

Analysis of PDEs · Mathematics 2020-01-03 Eduard Feireisl , Martina Hofmanová

The Euler-Maxwell system as a hydrodynamic model for plasma physics to describe the dynamics of the compressible electrons in a constant charged non-moving ion background is studied. The global smooth flow with small amplitude is…

Analysis of PDEs · Mathematics 2011-07-12 Renjun Duan

The goal of this work is to investigate the almost pressureless Euler-Poisson (EP) system with repulsive force in the large friction limit. The leading order equations in the limit are shown to be the hyperbolic-elliptic Keller-Segel (KS)…

Analysis of PDEs · Mathematics 2026-03-20 Xin Liu

We study the convergence of a discrete Luenberger observer for the barotropic Euler equations in one dimension, for measurements of the velocity only. We use a mixed finite element method in space and implicit Euler integration in time. We…

Numerical Analysis · Mathematics 2026-03-13 Aidan Chaumet , Jan Giesselmann

We establish the global-in-time existence of solutions of finite relative-energy for the multidimensional compressible Euler-Poisson equations for plasma with doping profile for large initial data of spherical symmetry. Both the total…

Analysis of PDEs · Mathematics 2023-09-07 Gui-Qiang G. Chen , Lin He , Yong Wang , Difan Yuan

We establish the existence and compactness of global martingale entropy solutions with finite relative-energy for the stochastically forced system of isentropic Euler equations governed by a general pressure law. To achieve these, a…

Analysis of PDEs · Mathematics 2025-12-30 Gui-Qiang G. Chen , Feimin Huang , Danli Wang

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

An implicit Euler finite-volume scheme for a degenerate cross-diffusion system describing the ion transport through biological membranes is analyzed. The strongly coupled equations for the ion concentrations include drift terms involving…

Numerical Analysis · Mathematics 2018-01-30 Clément Cancès , Claire Chainais-Hillairet , Anita Gerstenmayer , Ansgar Jüngel

This paper is concerned with the Cauchy problem of the 3D compressible bipolar Navier--Stokes--Poisson (BNSP) system with unequal viscosities, and our main purpose is three--fold: First, under the assumption that $H^l\cap L^1$($l\geq…

Analysis of PDEs · Mathematics 2021-04-20 Qing Chen , Guochun Wu , Yinghui Zhang

Global stability of the spherically symmetric nonisentropic compressible Euler equations with positive density around global-in-time background affine solutions is shown in the presence of free vacuum boundaries. Vacuum is achieved despite…

Analysis of PDEs · Mathematics 2021-06-03 Calum Rickard