# Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium

## TL;DR

This paper analyzes the long-term behavior of solutions to the second order linearized Vlasov-Poisson equations near homogeneous equilibria, revealing nonlinear phenomena like Best frequencies with supporting numerical results.

## Contribution

It provides a detailed asymptotic analysis of the second order linearized Vlasov-Poisson system, highlighting nonlinear effects and introducing numerical validation.

## Key findings

- Identification of Best frequencies in the system
- Numerical validation in 1Dx1D and 2Dx2D cases
- Detailed asymptotic description of long-time behavior

## Abstract

The asymptotic behavior of the solutions of the second order linearized Vlasov-Poisson system around homogeneous equilibria is derived. It provides a fine description of some nonlinear and multidimensional phenomena such as the existence of Best frequencies. Numerical results for the 1Dx1D and 2Dx2D Vlasov-Poisson system illustrate the effectiveness of this approach.