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

Chuqi Cao; Dingqun Deng; Xingyu Li

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arXiv · 2111.05569

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

Chuqi Cao·Dingqun Deng·Xingyu Li

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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 $H^2_{x, v}( \langle v \rangle^k)$ 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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Chuqi Cao, Dingqun Deng, Xingyu Li. 2021-11-10. The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation near Maxwellian. https://arxiv.org/abs/2111.05569

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