论文标题
筛选的vlasov-Poisson系统围绕Penrose稳定平衡的衍生估计值
Derivative estimates for screened Vlasov-Poisson system around Penrose-stable equilibria
论文作者
论文摘要
在本文中，我们建立了Vlasov-Poisson系统的衍生估计值，并在相位空间上围绕Penrose稳定平衡进行筛选相互作用$ \ MATHBB {r}^d_x \ times \ times \ times \ mathbb {r} _v^d $，并带有dimension $ d \ ge 3 $。特别是，我们确定了扰动系统密度较高衍生物的最佳衰减估计值，就像自由运输一样，直至时间校正。这将Han-Kwan，Nguyen和Rousset的最新工作扩展到密度的较高衍生物。该证明利用了\ cite {t-r-hk}对线性问题中强迫项的结构的几个关键观察，并使用诱导参数来对衍生估计中出现的所有术语进行分类。
In this paper, we establish derivative estimates for the Vlasov-Poisson system with screening interactions around Penrose-stable equilibria on the phase space $\mathbb{R}^d_x\times \mathbb{R}_v^d$, 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 \cite{T-R-HK} by Han-Kwan, Nguyen and Rousset to higher derivatives of the density. The proof makes use of several key observations from \cite{T-R-HK} on the structure of the forcing term in the linear problem, with induction arguments to classify all the terms appearing in the derivative estimates.
