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 μ. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space H2x, v( v k) for some constant k >0. The proof is based on extra dissipation generated from semigroup method and energy estimates on electrostatic field.
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