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.

中文翻译：

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彭罗斯稳定平衡附近的筛选Vlasov-Poisson系统的导数估计

在本文中，我们通过筛选相空间$ {\ mbox {Re}} ^ d_x \ times {\ mbox {Re}} _ v ^ d $上彭罗斯稳定平衡附近的相互作用，建立Vlasov-Poisson系统的导数估计，尺寸为$ d \ ge 3 $。尤其是，我们建立了对扰动系统密度的更高导数的最佳衰减估计，正像自由传输一样，直到时间的对数校正。这扩展了最近的工作[13]由Han-Kwan，Nguyen和Rousset提出，以提高密度的导数。该证明利用了[13线性问题中强迫项的结构，并用归纳论证对所有出现在导数估计中的项进行分类。