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. 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. 2021. ⟨hal-03427367v1⟩