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Related papers: The Nonrelativistic Limit of Relativistic Vlasov-M…

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We deal with the ``nonrelativistic limit'', i.e. the limit c to infinity, where c is the speed of light, of the nonlinear PDE system obtained by coupling the Dirac equation for a 4-spinor to the Maxwell equations for the self-consistent…

Analysis of PDEs · Mathematics 2007-05-23 Philippe Bechouche , Norbert J. Mauser , Sigmund Selberg

We prove that solutions of the 3D relativistic Vlasov-Maxwell system can be extended, as long as the quantity $\sigma_{-1}(t, x) = \max_{|\omega|=1} \,\int_{R^3} \frac{dp}{\sqrt{1+p^2}}\, \frac{1}{(1+v\cdot\omega)}\, f(t, x, p)$ is bounded…

Analysis of PDEs · Mathematics 2014-06-09 Markus Kunze

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 examine numerically and analytically the problem of the relativistic velocity distribution in a 1-dim relativistic gas in thermal equilibrium. Our derivation is based on the special theory of relativity, the central limit theorem and the…

Data Analysis, Statistics and Probability · Physics 2016-01-25 Evaldo M. F. Curado , Felipe T. L. Germani , Ivano Damiao Soares

The relativistic Boltzmann equation for a constant differential cross section and with periodic boundary conditions is considered. The speed of light appears as a parameter $c>c_0$ for a properly large and positive $c_0$. A local existence…

Mathematical Physics · Physics 2009-11-10 Simone Calogero

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 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 prove almost sharp decay estimates for the small data solutions and their derivatives of the Vlasov-Maxwell system in dimension $n \geq 4$. The smallness assumption concerns only certains weighted $L^1$ or $L^2$ norms of the initial…

Analysis of PDEs · Mathematics 2019-03-12 Léo Bigorgne

We show that weak solutions of the relativistic Vlasov-Maxwell system preserve the total energy provided that the electromagnetic field is locally of bounded variation and, for any $\lambda$> 0, the one-particle distribution function has a…

Analysis of PDEs · Mathematics 2012-09-04 Reinel Sospedra-Alfonso

We derive relativistic Maxwell-Bloch equations for potential applications in astronomical environments, where various radiative processes are known to occur, including the maser action and Dicke's superradiance. We show that for both…

Quantum Physics · Physics 2026-04-15 Ningyan Fang , Victor Botez , Fereshteh Rajabi , Martin Houde

We prove the global asymptotic stability of the Minkowski space for the massless Einstein-Vlasov system in wave coordinates. In contrast with previous work on the subject, no compact support assumptions on the initial data of the Vlasov…

Analysis of PDEs · Mathematics 2022-09-27 Léo Bigorgne , David Fajman , Jérémie Joudioux , Jacques Smulevici , Maximilian Thaller

We study radially symmetric solutions to the 2D Vlasov-Maxwell system and construct solutions that initially possess arbitrarily small $C^k$ norms ($k \geq 1$) for the charge densities and the electric fields, but attain arbitrarily large…

Analysis of PDEs · Mathematics 2023-11-14 Katherine Zhiyuan Zhang

At least one dimensionless physical constant (i.e., a physically observable) must change for the cosmic time to make the varying speed of light (VSL) models phenomenologically feasible. Various physical constants and quantities also should…

Cosmology and Nongalactic Astrophysics · Physics 2023-05-04 Seokcheon Lee

We show that nonrelativsitic scaling of the collisionless Vlasov-Maxwell system implies the existence of a formal invariant slow manifold in the infinite-dimensional Vlasov-Maxwell phase space. Vlasov-Maxwell dynamics restricted to the slow…

Plasma Physics · Physics 2021-07-01 George Miloshevich , Joshua W. Burby

We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the relativistic relative velocity for two colliding particles in a non-degenerate relativistic gas. The distribution reduces to Maxwell distribution for the relative…

Cosmology and Nongalactic Astrophysics · Physics 2014-06-02 M. Cannoni

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 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

In this paper we study the large-time behavior of classical solutions to the two-species Vlasov-Maxwell-Boltzmann system in the whole space $\R^3$. The existence of global in time nearby Maxwellian solutions is known from [34] in 2006.…

Analysis of PDEs · Mathematics 2016-02-22 Renjun Duan , Robert M. Strain

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

Euler--Maxwell systems describe the dynamics of inviscid plasmas. In this work, we consider an incompressible two-dimensional version of such systems and prove the existence and uniqueness of global weak solutions, uniformly with respect to…

Analysis of PDEs · Mathematics 2025-06-04 Diogo Arsénio , Haroune Houamed