A note on Landau damping of two-species Vlasov–Poisson system

Abstract

Abstract In this note we adopt an approach by Grenier et al (2021 Math. Res. Lett. 28 1679–1702) for studying the nonlinear Landau damping of the two-species Vlasov–Poisson system in the phase space T x d × R v d with the dimension d ⩾ 1 . The main goal is twofold: one is to extend the one-species case to the two-species case where the electron mass is finite and the ion mass is sufficiently large, and the other is to modify the G -functional such that it involves the norm in L d + 1 instead of L 2 as well as derivatives up to only the first order.