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This article is devoted to the Relativistic Vlasov-Maxwell system in space dimension three. We prove the local smooth solvability for weak topologies (and its long time version for small data). This result is derived from a representation…

Analysis of PDEs · Mathematics 2023-06-22 Christophe Cheverry , Slim Ibrahim

The Cauchy problem for the Vlasov-Maxwell-Boltzmann equations (VMB) is considered. First the renormalized solution to the Vlasov equation with the Lorentz force is discussed and the difficulty on the partial differentiability of the…

Analysis of PDEs · Mathematics 2011-01-11 Xianpeng Hu , Dehua Wang

The physical essence of the non-relativistic limit, from the relativistic Vlasov-Maxwell-Landau system to the Vlasov-Poisson-Landau system, lies in the transition from finite-speed electromagnetic waves to instantaneous Coulomb…

Analysis of PDEs · Mathematics 2025-11-25 Chuqi Cao , Ling-Bing He , Yuanjie Lei , Qinghua Xiao

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption…

Analysis of PDEs · Mathematics 2016-04-18 Robert Glassey , Stephen Pankavich , Jack Schaeffer

We consider relativistic plasma particles subjected to an external gravitation force in a $3$D half space whose boundary is a perfect conductor. When the mean free path is much bigger than the variation of electromagnetic fields, the…

Analysis of PDEs · Mathematics 2022-03-04 Yunbai Cao , Chanwoo Kim

The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma…

Mathematical Physics · Physics 2021-03-23 Jörg Weber

The relativistic Vlasov-Maxwell system is a kinetic model for collisionless plasmas. For the two-dimensional model, global well-posedness of this model is known and was proven by deriving global bounds on the momentum support of the…

Analysis of PDEs · Mathematics 2024-11-28 Matthew Hernandez , Neel Patel , Elena Salguero

The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the…

Mathematical Physics · Physics 2011-11-10 Simone Calogero

We consider the three-dimensional relativistic Vlasov-Maxwell-Boltzmann system, where the speed of light $c$ is an arbitrary constant no less than 1, and we establish global existence and nonlinear stability of the vacuum for small initial…

Analysis of PDEs · Mathematics 2026-02-06 Chuqi Cao , Xingyu Li

Consider the relativistic Vlasov-Maxwell-Boltzmann system describing the dynamics of an electron gas in the presence of a fixed ion background. Thanks to recent works \cite{Germain-Masmoudi-ASENS-2014, Guo-Ionescu-Pausader-JMP-2014} and…

Analysis of PDEs · Mathematics 2023-01-11 Yan Guo , Qinghua Xiao

We study the instability of solutions to the relativistic Vlasov-Maxwell systems in two limiting regimes: the classical limit when the speed of light tends to infinity and the quasineutral limit when the Debye length tends to zero. First,…

Analysis of PDEs · Mathematics 2017-07-20 Daniel Han-Kwan , Toan T. Nguyen

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle…

Analysis of PDEs · Mathematics 2009-12-31 Robert Glassey , Stephen Pankavich , Jack Schaeffer

A global solvability result of the Cauchy problem of the two-species Vlasov-Maxwell-Landau system near a given global Maxwellian is established by employing an approach different than that of [5]. Compared with that of [5], the minimal…

Analysis of PDEs · Mathematics 2013-09-26 Yuanjie Lei , Huijiang Zhao

We study existence and uniqueness of the solution to the gravitational Vlasov-Poisson system evolving in $\mathbb{R}^3$. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in…

Analysis of PDEs · Mathematics 2024-07-16 Guido Cavallaro , Carlo Marchioro

The Einstein-Vlasov-Maxwell (EVM) system can be viewed as a relativistic generalization of the Vlasov-Poisson (VP) system. As it is proved below, one of nice property obeys by the first system is that the strong energy condition holds and…

General Relativity and Quantum Cosmology · Physics 2007-05-23 P. Noundjeu

In a previous paper two of the authors (G. R. and A. D. R.) showed that there exist global, classical solutions of the spherically symmetric Vlasov-Einstein system for small initial data. The present paper continues this investigation and…

General Relativity and Quantum Cosmology · Physics 2015-06-25 Gerhard Rein , Alan D. Rendall , Jack Schaeffer

The Cauchy problem is revisited for the so-called relativistic Vlasov-Poisson system in the attractive case. Global existence and uniqueness of spherical classical solutions is proved under weaker assumptions than previously used. A new…

Mathematical Physics · Physics 2009-02-06 Michael K. -H. Kiessling , A. Shadi Tahvildar-Zadeh

A global-in-time existence theorem for classical solutions of the Vlasow-Darwin system is given under the assumption of smallness of the initial data. Furthermore it is shown that in case of spherical symmetry the system degenerates to the…

Mathematical Physics · Physics 2009-01-26 M. Seehafer

In this article the static Einstein-Vlasov-Maxwell system is considered in spherical symmetry. This system describes an ensemble of charged particles interacting by general relativistic gravity and Coulomb forces. First, a proof for local…

General Relativity and Quantum Cosmology · Physics 2019-10-09 Maximilian Thaller

The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass…

Analysis of PDEs · Mathematics 2019-02-26 Klemens Fellner , Jeff Morgan , Bao Quoc Tang