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One-species Vlasov-Poisson-Landau system near Maxwellians in the whole space

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  • The classical one-species Vlasov-Poisson-Landau system describes dynamics of electrons interacting with its self-consistent electrostatic field as well as its grazing collisions modeled by the famous Landau (Fokker-Planck) collision kernel. We show in this manuscript that the Cauchy problem for the one-species Vlasov-Poisson-Landau system which includes the Coulomb potential admits a unique global solution near a given global Maxwellian in the whole space $\mathbb{R}^3_x$ provided that the initial perturbation satisfies certain regularity and smallness conditions. Compared with that of [12], which, to the best of our knowledge, is the only result concerning the one-species Vlasov-Poisson-Landau system available up to now, we do not ask the initial perturbation to satisfy the neutral condition and the minimal regularity assumption we imposed on the initial perturbation is also weaker.
    Mathematics Subject Classification: Primary: 35Q83, 35B40, 82C40.


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