Joint BCAM-UPV/EHU Analysis and PDE seminar: The Vlasov-Poisson-Boltzmann/Landau equation with polynomial perturbation near Maxwellian

Date: Thu, Jul 7 2022

Hour: 17:00

Location: BCAM Seminar room and Online

Speakers: Xingyu Li

LOCATION: BCAM Seminar room and Online

We consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space $H^2_{x,v}(⟨v⟩k)$ 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 the semigroup method and energy estimates on electrostatic fields. It is a joint work with Chuqi Cao and Dingqun Deng (Tsinghua University).

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Confirmed speakers:

Xingyu Li