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

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.