Related papers: Weak collision effect on nonlinear Landau damping …
In this paper, we study the Vlasov-Poisson-Fokker-Planck (VPFP) equation with a small collision frequency $0 < \nu \ll 1$, exploring the interplay between the regularity and size of perturbations in the context of the asymptotic stability…
Consider the Vlasov-Poisson-Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu…
In this paper, we study the Vlasov-Poisson-Landau Equations on $\mathbb{T}^3\times \mathbb{R}^3$ with small collision frequency $\nu\ll 1$. We prove that for $\nu$-independent perturbations of the global Maxwellians in Gevrey-$2_-$,…
In this paper, we give an elementary proof of the nonlinear Landau damping for the Vlasov-Poisson system near Penrose stable equilibria on the torus $\mathbb{T}^d \times \mathbb{R}^d$ that was first obtained by Mouhot and Villani in…
In this article we study the problem of nonlinear Landau damping for the Vlasov-Poisson equations on the torus. As our main result we show that for perturbations initially of size $\epsilon>0$ and time intervals $(0,\epsilon^{-N})$ one…
This paper studies the nonlinear Landau damping on the torus $\mathbb{T}^d$ for the Vlasov-Poisson system with massless electrons (VPME). We consider solutions with analytic or Gevrey ($\gamma > 1/3$) initial data, close to a homogeneous…
We analyse the effect of expansion in Newtonian cosmology on the asymptotic behaviour of charged self-interacting plasmas close to Poisson equilibria. To this end, we study the Vlasov-Poisson system on the phase space of a $3$-torus which…
We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (both on the torus and on $\mathbb{R}^3$) linearized around a sufficiently nice, spatially uniform kinetic…
In this paper, we study Landau damping in the weakly collisional limit of a Vlasov-Fokker-Planck equation with nonlinear collisions in the phase-space $(x,v) \in \mathbb T_x^n \times \mathbb R^n_v$. The goal is four-fold: (A) to understand…
We examine the phenomenon of Landau Damping in relativistic plasmas via a study of the relativistic Vlasov-Poisson system (rVP) on the torus for initial data sufficiently close to a spatially uniform steady state. We find that if the steady…
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near…
In this paper, we consider the linearized Vlasov-Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter $\eps$ in front of the collision operator which will tend to $0$. Moreover,…
We investigate nonlinear Landau damping for the two-species screened Vlasov-Poisson system with large initial distributions on the phase space $\mathbb{R}^d \times \mathbb{R}^d$ (where $d \geq 3$). Under a structural quasi-neutrality…
We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are small perturbations of homogeneous Penrose-stable equilibria. We also prove the…
We prove global existence of smooth solutions near Maxwellians for the non-cutoff Vlasov-Poisson-Boltzmann system in the weakly collisional regime. To address the weak dissipation of the non-cutoff linearized Boltzmann operator, we develop…
We address the long time behaviour of weakly interacting diffusive particle systems on the d-dimensional torus. Our main result is to show that, under certain regularity conditions, the weak error between the empirical distribution of the…
Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for…
We show that the linearized Vlasov-Poisson equations around self-similar non-homogeneous states near zero contain the full plasma echo mechanism, yielding Gevrey 3 as a critical stability class. Moreover, here Landau damping may persist…
In this paper, we study the optimal stability threshold for the Vlasov-Poisson equation with weak Fokker-Planck collision. We prove that if the initial perturbation is of size $\nu^{\frac{1}{2}}$ in the critical weighted space…
This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational…