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

2021/11/10 by Cao, Chuqi, Deng, Dingqun, Li, Xingyu
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.05569

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 μ. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space H²_{x, v}( ⟨ 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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