In this note we adopt an approach by Grenier, Nguyen and Rodnianski in {GNR} for studying the nonlinear Landau damping of the two-species Vlasov-Poisson system in the phase space Tᵈₓ × Rᵈᵥ 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 Lᵈ⁺¹ instead of L² as well as derivatives up to only the first order.
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Duan et al. (2024) studied this question.
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