We consider the Vlasov-Poisson system in a 1d periodic setting, and consider the stability of steady states. The simplest family corresponds to homogeneous steady states, and a lot of literature has been devoted to their study. When a Penrose-type criterion is satisfied, following works of Mouhot-Villani and later works, perturbations are damped, when the Penrose criterion is violated, the situation is more complicated and related to another class of steady states: the (inhomogeneous) BGK waves.
Co-authors: Dongfen Bian, Emmanuel Grenier, Wenrui Huang
By Matthew Juniper
By Sergey Gavrilyuk
By David Lannes
