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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

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 relativistic Vlasov-Maxwell system in three dimensions and study the limiting asymptotic behavior as $t \to \infty$ of solutions launched by small, compactly supported initial data. In particular, we prove that such…

Analysis of PDEs · Mathematics 2024-03-12 Stephen Pankavich , Jonathan Ben-Artzi

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 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

We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces…

Analysis of PDEs · Mathematics 2016-03-16 Pierre-Emmanuel Jabin , Maxime Hauray

Convergence of particle systems to the Vlasov-Navier-Stokes equations is a difficult topic with only fragmentary results. Under a suitable modification of the classical Stokes drag force interaction, here a partial result in this direction…

Probability · Mathematics 2018-07-31 Franco Flandoli , Marta Leocata , Cristiano Ricci

We consider linear stability of steady states of 1(1/2) and 3D Vlasov-Maxwell systems for collisionless plasmas. The linearized systems can be written as separable Hamiltonian systems with constraints. By using a general theory for…

Analysis of PDEs · Mathematics 2021-07-28 Zhiwu Lin

In this paper, we present a rigorous derivation of the mean-field limit for a moderately interacting particle system in $\R^d$ $(d\geq 2)$. For stochastic initial data, we demonstrate that the solution to the interacting particle model,…

Analysis of PDEs · Mathematics 2024-07-08 Jinhuan Wang , Mengdi Zhuang , Hui Huang

The Vlasov-Maxwell-Boltzmann system is a fundamental model to describe the dynamics of dilute charged particles, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of…

Analysis of PDEs · Mathematics 2010-05-02 Robert M. Strain

We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium…

Probability · Mathematics 2013-09-19 Francois Bolley , Arnaud Guillin , Florent Malrieu

We consider the $3$-dimensional relativistic Vlasov-Maxwell system with data without compact support in momentum space. We prove two continuation criteria for solutions to this system. First, we show that a regular solution can be continued…

Analysis of PDEs · Mathematics 2016-02-22 Jonathan Luk , Robert M. Strain

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

For more than half a century, most of the plasma scientists have encountered a violation of the conservation laws of charge, momentum, and energy whenever they have numerically solve the first-principle equations of kinetic plasmas, such as…

Plasma Physics · Physics 2018-11-15 Takashi Shiroto , Naofumi Ohnishi , Yasuhiko Sentoku

While a fully relativistic collisionless plasma is modeled by the Vlasov-Maxwell system a good approximation in the non-relativistic limit is given by the Vlasov-Poisson system. We modify the Vlasov-Poisson system so that damping due to the…

Mathematical Physics · Physics 2016-04-21 Sebastian Bauer

We construct global-in-time classical solutions to the nonlinear Vlasov-Maxwell system in a three-dimensional half-space beyond the vacuum scattering regime. Our approach combines the construction of stationary solutions to the associated…

Analysis of PDEs · Mathematics 2025-10-07 Jin Woo Jang , Chanwoo Kim

The Vlasov--Maxwell equations are used for the kinetic description of magnetized plasmas. As they are posed in an up to 3+3 dimensional phase space, solving this problem is extremely expensive from a computational point of view. In this…

Numerical Analysis · Mathematics 2020-01-29 Lukas Einkemmer , Alexander Ostermann , Chiara Piazzola

The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of…

We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell system that possess arbitrarily large charge densities and electric fields. In particular, we construct spherically symmetric solutions that describe a thin shell…

Mathematical Physics · Physics 2018-07-10 Jonathan Ben-Artzi , Simone Calogero , Stephen Pankavich