Related papers: Sharp asymptotic behavior of solutions of the $3d$…
This paper is concerned with the asymptotic properties of the small data solutions to the massless Vlasov-Maxwell system in $3d$. We use vector field methods to derive almost optimal decay estimates in null directions for the…
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…
This paper is concerned with the asymptotic behavior of small data solutions to the three-dimensional Vlasov-Maxwell system in the exterior of a light cone. The plasma does not have to be neutral and no compact support assumptions are…
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,…
This paper is devoted to the study of relativistic Vlasov-Maxwell system in three space dimension. For a class of large initial data, we prove the global existence of classical solution with sharp decay estimate. The initial Maxwell field…
The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this…
In this paper, we study pointwise decay estimates in time for Vlasov fields on non-trapping asymptotically hyperbolic manifolds. We prove optimal decay estimates in time for the spatial density induced by Vlasov fields on these geometric…
We study the asymptotic behavior of solutions to the Vlasov equation in the presence of a strong external magnetic field. In particular we provide a mathematically rigorous derivation of the guiding-center approximation in the general three…
The aim of this article is to demonstrate how the vector field method of Klainerman can be adapted to the study of transport equations. After an illustration of the method for the free transport operator, we apply the vector field method to…
In this article, we present a vector field method for the study of solutions to massless relativistic transport equations. Compared to the methodologie developped by Fajman-Joudioux-Smulevici, we remove the Lorentz boosts of the commutation…
We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small gas, i.e.\ measures of the form $\delta_{(\mathcal{X}(t),\mathcal{V}(t))}+\mu^2d{\bf x}d{\bf v}$ for some $(\mathcal{X},…
In this paper, we present sharp decay estimates for small data solutions of the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on a…
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…
We consider the repulsive Vlasov-Poisson system in dimension $d \geq 4$. A sufficient condition on the decay rate of the associated electric field is presented that guarantees the scattering and determination of the complete asymptotic…
This paper investigates the asymptotic behavior of solutions to the steady pressure-free Prandtl system. By employing a modified von Mises transformation, we rigorously prove the far-field convergence of Prandtl solutions to Blasius flow. A…
Given any smooth, suitably small initial data, which decays polynomially at infinity, we prove global regularity for the $3D$ relativistic massive Vlasov-Maxwell system. In particular, the compact support assumption, which is widely used in…
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.…
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…
In this paper, we study small data solutions for the Vlasov-Poisson system with the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flow. We prove sharp decay estimates in space and time for…
We show that the simplified $3D$ relativistic Vlasov-Maxwell (sRVM) system, in which there is no magnetic field, poses a global solution for a class of arbitrarily large cylindrically symmetric initial data. In particular, a vanishing order…