Abstract
In this paper, we establish derivative estimates for the Vlasov-Poisson system with screening interactions around Penrose-stable equilibria on the phase space \begin{document}$ {\mbox{Re }}^d_x\times {\mbox{Re }}_v^d $\end{document} , with dimension \begin{document}$ d\ge 3 $\end{document} . 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.
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