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Derivative estimates for screened Vlasov-Poisson system around Penrose-stable equilibria

The author would like to thank Toan T. Nguyen for his many insightful discussions on the subject. The research was supported by the NSF under grant DMS-1764119

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  • In this paper, we establish derivative estimates for the Vlasov-Poisson system with screening interactions around Penrose-stable equilibria on the phase space $ {\mbox{Re }}^d_x\times {\mbox{Re }}_v^d $, with dimension $ d\ge 3 $. In particular, we establish the optimal decay estimates for higher derivatives of the density of the perturbed system, precisely like the free transport, up to a log correction in time. This extends the recent work [13] by Han-Kwan, Nguyen and Rousset to higher derivatives of the density. The proof makes use of several key observations from [13] on the structure of the forcing term in the linear problem, with induction arguments to classify all the terms appearing in the derivative estimates.

    Mathematics Subject Classification: Primary: 35B35, 35B40, 35Q83.


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