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

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 $d\ge 3$). 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.

50 pages, all comments are welcome