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

Chuqi Cao (1) , Dingqun Deng (1) , Xingyu Li (2, 3)

1 Yau Mathematical Sciences Center, Tsinghua University,
2 Université Paris Dauphine-PSL
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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$H^2_{x,v} (\langle v\rangle^ k)$ for some constant k > 0. For the domain union of cubes, We will consider the specular-reflection boundary condition and its high-order compatible specular boundary condition. The proof is based on extra dissipation generated from semigroup method and energy estimates on electrostatic field.

Domaines: Mathématiques [math]

Chuqi Cao, Dingqun Deng, Xingyu Li. The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian. 2022. ⟨hal-03427367v2⟩