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

Abstract: 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 $\mu$. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space $H^2_{x, v}( \langle v \rangle<sup>k)$ for some constant $k &gt;0$. The proof is based on extra dissipation generated from semigroup method and energy estimates on electrostatic field.