论文标题
在$ \ mathbb {r}^d $，$ d \ geq3 $中，围绕penrose稳定均衡的vlasov-poisson系统的尖锐估计值
Sharp estimates for screened Vlasov-Poisson system around Penrose-stable equilibria in $\mathbb{R}^d $, $ d\geq3$
论文作者
论文摘要
在本文中，我们研究了penrose稳定平衡的渐近稳定性，在$ \ mathbb {r}^d $中使用$ d \ geq 3 $中的vlasov-poisson系统的解决方案中，该系统最初由bedrossian，masmoudi，masmoudi和mouhot in \ cite in \ cite {更确切地说，我们证明了扰动系统密度的尖锐衰减估计，就像仅使用Hölder的免费传输（即$ c^{a} $，$ 0 <a <a <1 $）扰动初始数据。这改善了Han-Kwan，Nguyen的\ Cite {Hankwand2021}的最新作品，并改善了密度的下部衍生物的rousset，以及T. nguyen的较高衍生物，用于较高的衍生物，用于较高的衍生物。此外，我们为线性化问题建立了内核的新估计和取消，以获得此结果。此外，我们还证明了Vlasov-Poisson系统的结果，在该系统中，电场遵守包含无质量电子/离子情况的一般非线性泊松方程。
In this paper, we study the asymptotic stability of Penrose-stable equilibria among solutions of the screened Vlasov-Poisson system in $\mathbb{R}^d$ with $d\geq 3$ that was first established by Bedrossian, Masmoudi, and Mouhot in \cite{JBedrossian2018} with smooth initial data. More precisely, we prove the sharp decay estimates for the density of the perturbed system, exactly like the free transport with only Hölder (i.e., $C^{a}$ for $0<a<1$) perturbed initial data. This improves the recent works in \cite{HanKwanD2021} by Han-Kwan, Nguyen, and Rousset for lower derivatives of the density and in \cite{NguyenTT2020} by T. Nguyen for higher derivatives with a logarithmic correction in time. Furthermore, we establish new estimates and cancellations of the kernel to the linearized problem to obtain this result. Moreover, we also prove this result for the Vlasov-Poisson system in which the electric field obeys a general nonlinear Poisson equation containing massless electrons/ions case.
