Nonlinear Landau damping for the two-species screened Vlasov-Poisson system with large initial distributions

TL;DR

This paper proves nonlinear Landau damping for the two-species screened Vlasov-Poisson system with large initial data, establishing global solutions, stability of equilibria, and optimal decay rates in high-dimensional space.

Contribution

It is the first to demonstrate Landau damping for large initial distributions in the two-species Vlasov-Poisson system, confirming stability and decay in the whole space.

Findings

Existence and uniqueness of global strong solutions for large initial data.

Time-asymptotic stability of Penrose-stable equilibria.

Optimal decay rate of t^{-d} for the net charge density.

Abstract

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 condition, we establish the existence and uniqueness of global strong solutions to the two-species system with arbitrarily large initial distributions. Furthermore, we prove the time-asymptotic stability of Penrose-stable equilibria and establish the optimal decay rate $t^{-d}$ for the net charge density, thereby verifying the nonlinear Landau damping effect for the two-species screened Vlasov-Poisson system in the whole space. To the best of our knowledge, this represents the first result on Landau damping for the two-species Vlasov-Poisson system with large initial distributions that are significantly far from equilibrium.