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The Gevrey Regularity for the Vlasov–Poisson–Landau and the Non-cutoff Vlasov–Poisson–Boltzmann Systems

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Abstract

We study the Vlasov–Poisson–Boltzmann system without angular cutoff and the Vlasov–Poisson–Landau system with all hard potentials in the perturbation setting, and establish the Gevrey smoothness in both spatial and velocity variables for a class of low-regularity weak solutions. This work extends the results by Duan–Li–Liu [16] for the pure Boltzmann equation to the case of the Vlasov–Poisson–Boltzmann/Landau systems.

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Acknowledgements

Hao Wang was supported by NSFC (Nos.12301284).

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  1. Department of Mathematical Sciences, Tsinghua University, Bei**g, 100084, China

    Hao Wang

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Wang, H. The Gevrey Regularity for the Vlasov–Poisson–Landau and the Non-cutoff Vlasov–Poisson–Boltzmann Systems. J Stat Phys 190, 197 (2023). https://doi.org/10.1007/s10955-023-03208-1

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