The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian

Abstract

In this work, we consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian $\mu$. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space $H_{x,v}^2(⟨v{⟩}^k)$ for some constant $k>0$. The proof is based on extra dissipation generated from semigroup method and energy estimates on electrostatic field.

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