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arXiv · 2012.10845

Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff

Dingqun Deng
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Abstract

In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space $\mathbb{R}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions is known for soft potential from [15]. However the smoothing effect of these solutions has been a challenging open problem. We establish the global existence and regularizing effect to the Cauchy problem for hard potential with large time decay. Hence, the solutions are smooth with respect to $(t,x,v)$ for any positive time $t>0$. This gives the regularity to Vlasov-Poisson-Boltzmann system, which enjoys a similar smoothing effect as Boltzmann equation. The proof is based on the time-weighted energy method building also upon the pseudo-differential calculus.

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Dingqun Deng. 2020-12-20. Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff. https://doi.org/10.1007/s00220-021-04209-5

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