The low-regularity solutions to the Vlasov-Poisson-Landau systems in the whole space

In this paper, we investigate the Vlasov-Poisson-Landau system in the whole space. Our primary objective is to establish the global existence and algebraic time-decay rates of mild solutions to the Vlasov-Poisson-Landau system near Maxwellians. These results are valid under the assumption that the initial data satisfy specific smallness conditions within the function space $ L^1_kL^\infty_TL^2_v \cap L^p_kL^\infty_TL^2_v $. Our analytical framework is inspired by the methodology developed by Duan et al. (SIAM J. Math. Anal. 56 (2024), no. 1,762-800.).