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We analyse a reduced 1D Vlasov--Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split in two terms: an…

Analysis of PDEs · Mathematics 2016-08-16 José A. Carrillo , Simon Labrunie

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 dynamics of dilute plasma particles such as electrons and ions can be modeled by the fundamental two species Vlasov-Poisson-Boltzmann equations, which describes mutual interactions of plasma particles through collisions in the…

Analysis of PDEs · Mathematics 2025-04-01 Zaihong Jiang , Yong Wang , Hang Xiong

By identifying a norm capturing the effect of the forcing governed by the Poisson equation, we give a detailed spectrum analysis on the linearized Vlasov-Poisson-Boltzmann system around a global Maxwellian. It is shown that the electric…

Analysis of PDEs · Mathematics 2014-02-18 Hailiang Li , Tong Yang , Mingying Zhong

This article is devoted to the kinetic description in phase space of magnetically confined plasmas. It addresses the problem of stability near equilibria of the Relativistic Vlasov Maxwell system. We work under the Glassey-Strauss compactly…

Analysis of PDEs · Mathematics 2021-03-16 Christophe Cheverry , Slim Ibrahim , Dayton Preissl

We set up and analyze a model of radiation damping within the framework of continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to Blanchet, Damour and Schaefer. In order to simplify the problem as much as possible…

Mathematical Physics · Physics 2015-06-26 Markus Kunze , Alan D. Rendall

In the paper, we are concerned with the nonlinear Cauchy problem on the Vlasov-Poisson-Landau/Boltzmann system around global Maxwellians in torus or finite channel. The main goal is to establish the global existence and large time behavior…

Analysis of PDEs · Mathematics 2024-02-08 Dingqun Deng , Renjun Duan

We construct the global unique solution near a global Maxwellian to the Vlasov-Poisson-Landau system in the whole space. The total density of two species of particles decays at the optimal algebraic rates as the Landau equation in the whole…

Analysis of PDEs · Mathematics 2015-09-29 Yanjin Wang

We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…

Analysis of PDEs · Mathematics 2024-07-02 Timothée Crin-Barat , Yue-Jun Peng , Ling-Yun Shou , Jiang Xu

This paper investigates the global dynamics of a three-dimensional fluid-particle interaction system that couples the compressible barotropic Navier-Stokes equations with the Vlasov-Fokker-Planck equation through a density-dependent…

Analysis of PDEs · Mathematics 2026-03-10 Fucai Li , Jinkai Ni , Dehua Wang

The motion of a fully ionized plasma of electrons and ions is generally governed by the Vlasov-Maxwell-Landau system. We prove the global existence of solutions near Maxwellians to the Cauchy problem of the system for the long-range…

Analysis of PDEs · Mathematics 2012-05-25 Renjun Duan

In this paper, we study the Cauchy problem for the linear and semilinear Moore-Gibson-Thompson (MGT) equation in the dissipative case. Concerning the linear MGT model, by utilizing WKB analysis associated with Fourier analysis, we derive…

Analysis of PDEs · Mathematics 2021-05-17 Wenhui Chen , Ryo Ikehata

The spatially homogeneous Vlasov-Nordstr\"{o}m-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of…

Analysis of PDEs · Mathematics 2024-09-10 Shengchuang Chang , Shuangqian Liu , Tong Yang

The purpose of this paper is twofold. In the first part, we provide a new proof of the global existence of the solutions to the Vlasov-Maxwell system with a small initial distribution function. Our approach relies on vector field methods,…

Analysis of PDEs · Mathematics 2025-03-05 Léo Bigorgne

We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small gas, i.e.\ measures of the form $\delta_{(\mathcal{X}(t),\mathcal{V}(t))}+\mu^2d{\bf x}d{\bf v}$ for some $(\mathcal{X},…

Analysis of PDEs · Mathematics 2022-07-13 Benoit Pausader , Klaus Widmayer , Jiaqi Yang

The classical problem of two uniformly charged infinite planes in electrochemical equilibrium with an infinite monovalent salt reservoir is solved exactly at the mean-field nonlinear Poisson-Boltzmann (PB) level, including an explicit…

Soft Condensed Matter · Physics 2009-11-07 M. N. Tamashiro , H. Schiessel

We investigate the global well-posedness of the ionic Vlasov-Poisson-Boltzmann system which models the evolution of dilute collisional ions. This system distinguishes the electronic Vlasov-Poisson-Boltzmann system via an additional…

Analysis of PDEs · Mathematics 2025-12-04 Fucai Li , Yichun Wang

This paper is concerned with the asymptotic properties of the small data solutions to the massless Vlasov-Maxwell system in $3d$. We use vector field methods to derive almost optimal decay estimates in null directions for the…

Analysis of PDEs · Mathematics 2020-12-14 Léo Bigorgne

Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…

Numerical Analysis · Mathematics 2013-10-24 Yingda Cheng , Irene M. Gamba , Fengyan Li , Philip J. Morrison

We study the Cauchy problem for the reduced Maxwell-Bloch equations with initial data for the electric field in weighted Sobolev spaces, assuming that all atoms initially reside in their ground state. Using the d-bar steepest descent…

Analysis of PDEs · Mathematics 2025-05-23 Kang Wu , Jingsong He , Yingcan Huang