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 $H^2_{x,v}(⟨v⟩k)$ 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).
Romain Duboscq, Ariane Trescases