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We study smooth, spherically-symmetric solutions to the Vlasov-Poisson system and relativistic Vlasov-Poisson system in the plasma physical case. We construct solutions that initially possess arbitrarily small C^k norms for the charge…

Analysis of PDEs · Mathematics 2019-10-15 Katherine Zhiyuan Zhang

In a recent paper Calogero and Alcantara derived a Lorentz-invariant Fokker-Planck equation, which corresponds to the evolution of a particle distribution associated with relativistic Brownian Motion. We study the "one and one-half"…

Analysis of PDEs · Mathematics 2015-09-01 Stephen Pankavich , Nicholas Michalowski

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 adapt the vector field method of Klainerman to the study of relativistic transport equations. First, we prove robust decay estimates for velocity averages of solutions to the relativistic massive and massless transport equations, without…

Analysis of PDEs · Mathematics 2018-03-16 David Fajman , Jérémie Joudioux , Jacques Smulevici

This paper focusses on the barely understood gap between the weakly nonlinear regime of structure formation and the onset of the virialized regime. While the former is accessed through perturbative calculations and the latter through…

Astrophysics · Physics 2007-05-23 Thomas Buchert

In (Arch. Rational. Mech. Anal 1986, 92:59-90), Glassey and Strauss showed that if the growth in the momentum of the particles is controlled, then the relativistic Vlasov-Maxwell system has a classical solution globally in time. Later they…

Mathematical Physics · Physics 2012-09-04 Reinel Sospedra-Alfonso , Reinhard Illner

We study the finite Larmor radius regime for the Vlasov-Poisson system. The magnetic field is assumed to be uniform. We investigate this non linear problem in the two dimensional setting. We derive the limit model by appealing to…

Analysis of PDEs · Mathematics 2015-11-03 Mihaï Bostan , Aurélie Finot , Maxime Hauray

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 fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original…

Mathematical Physics · Physics 2013-11-18 M. J. P. Cullen , D. K. Gilbert , B. Pelloni

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

A quasistatic nonlinear model for finite-strain poro-visco-elasticity is considered in the Lagrangian frame using Kelvin-Voigt rheology. The model consists of a mechanical equation which is coupled to a diffusion equation with a degenerate…

Analysis of PDEs · Mathematics 2024-08-28 Willem J. M. van Oosterhout

The relativistic generalization of the Newtonian Lagrangian perturbation theory is investigated. In previous works, the first-order trace solutions that are generated by the spatially projected gravitoelectric part of the Weyl tensor were…

General Relativity and Quantum Cosmology · Physics 2015-07-15 Alexandre Alles , Thomas Buchert , Fosca Al Roumi , Alexander Wiegand

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse…

Analysis of PDEs · Mathematics 2019-04-08 Yunbai Cao , Chanwoo Kim , Donghyun Lee

We use optimal transportation techniques to show uniqueness of the compactly supported weak solutions of the relativistic Vlasov-Darwin system. Our proof extends the method used by Loeper in J. Math. Pures Appl. 86, 68-79 (2006) to obtain…

Mathematical Physics · Physics 2012-09-04 Reinel Sospedra-Alfonso , Martial Agueh

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 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

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response…

High Energy Physics - Phenomenology · Physics 2024-11-08 Alessio Zaccone

In this paper, we introduce a new set of vector fields for the relativistic transport equation, which is applicable for general Vlasov-Wave type coupled systems. By combining the strength of Klainerman vector field method and Fourier…

Analysis of PDEs · Mathematics 2020-02-19 Xuecheng Wang

From a previous paper where we proposed a description of general relativity within the gravito-electromagnetic limit, we propose an alternative modified gravitational theory. As in the former version, we analyze the vector and tensor…

General Relativity and Quantum Cosmology · Physics 2022-05-03 Sergio Giardino

In this work, we consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian $\mu$. We establish the global existence, uniqueness and large time…

Analysis of PDEs · Mathematics 2024-05-29 Chuqi Cao , Dingqun Deng , Xingyu Li