The Non-cutoff Vlasov-Poisson-Boltzmann and Vlasov-Poisson-Landau Systems in Union of Cubes (2112.02315v2)

Abstract: This work concerns the Vlasov-Poisson-Boltzmann system without angular cutoff and Vlasov-Poisson-Landau system including Coulomb interaction in bounded domain, namely union of cubes. We establish the global stability, exponential large-time decay with specular-reflection boundary condition when an initial datum is near Maxwellian equilibrium. We provide the compatible specular boundary condition for high-order derivatives and a velocity weighted energy estimate.