Landau damping in dynamical Lorentz gases

In 2001 L. Bruneau and S. De Bièvre introduced an original model describing the interaction between a classical particle and an oscillating media. They showed (under some conditions) that for this model the media acts on the particle like a friction force. Here, I will present results about the Vlasov-Wave equation: the kinetic equation coming from their model.

Since in 2016 S. De bièvre, T. Goudon and A. Vavasseur showed that, under an appropriate scaling, the Vlasov-Wave equation is asymptotic to the attractive Vlasov-Poisson equation, it is natural to ask the question of the Landau damping for this model. First, I will recall the mechanisms of the Landau damping for the classical Vlasov equation and then I will explain how these mechanisms are modified in the Vlasov-Wave case. All these results will be illustrated by numerical simulations.