Related papers: Global existence and modified scattering for the s…
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…
We consider an asymptotic behavior of solutions to the Vlasov-Riesz system of order $\alpha$ in $\mathbb{R}^3$ which is a kinetic model induced by Riesz interactions. We prove small data scattering when $1/2<\alpha<1$ and modified…
We prove small data modified scattering for the Vlasov-Poisson system in dimension $d=3$ using a method inspired from dispersive analysis. In particular, we identify a simple asymptotic dynamic related to the scattering mass.
In this paper we prove the existence of a large class of periodic solutions of the Vlasov-Poisson in one space dimension that decay exponentially as t goes to infinity. The exponential decay is well known for the linearized version of the…
Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded…
We establish the global-in-time existence and uniqueness of classical solutions to the "one and one-half" dimensional relativistic Vlasov--Maxwell systems in a bounded interval, subject to an external magnetic field which is infinitely…
The existence of stationary solutions of the Einstein-Vlasov-Maxwell system which are axially symmetric but not spherically symmetric is proven by means of the implicit function theorem on Banach spaces. The proof generalises the methods of…
In $3+1$ dimensions, we study the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system. This system incorporates gravity, electromagnetic, weak and strong interactions for the initial stage of our universe. Due…
In this work, we consider the relativistic Vlasov-Maxwell system, linearized around a spatially homogeneous equilibrium, set in the whole space $\mathbb{R}^3 \times \mathbb{R}^3$. The equilibrium is assumed to belong to a class of radial,…
In 1989, R. DiPerna and P.-L. Lions established the existence of global weak solutions to the Vlasov-Maxwell system. In the present notes we give a somewhat simplified proof of this result for the relativistic version of this system, the…
In this paper we study the linearized Vlasov-Poisson equation for localized disturbances of an infinite, homogeneous Maxwellian background distribution in $\mathbb R^3_x \times \mathbb R^3_v$. In contrast with the confined case $\mathbb T^d…
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…
This paper proves almost-sharp asymptotics for small data solutions of the Vlasov-Nordstr\"om system in dimension three. This system consists of a wave equation coupled to a transport equation and describes an ensemble of relativistic,…
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…
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
As is well known from the work of R. Glassey} and J. Schaeffer, the main energy estimates which are used in global existence results for the gravitational Vlasov-Poisson system do not apply to the relativistic version of this system, and…
The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisions in the self-consistent electrostatic field. For cutoff…
We study the asymptotic behavior of small solutions to the Vlasov--Klein--Gordon system in high dimensions. The standard argument of Glassey and Strauss \cite{GS87} for studying small solutions to the Vlasov--Maxwell system does not apply…
In this paper, we establish the global existence of Lagrangian solutions to the ionic Vlasov--Poisson system under mild integrability assumptions on the initial data. Our approach involves proving the well-posedness of the…
We prove in the cases of spherical, plane and hyperbolic symmetry a local in time existence theorem and continuation criteria for cosmological solutions of the Einstein-Vlasov-scalar field system, with the sources generated by a…