A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM

doi:10.1007/s10473-025-0616-6

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (6): 2669-2684.doi: 10.1007/s10473-025-0616-6

A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM

Quoc-Hung NGUYEN^1,*, Dongyi WEI², Zhifei ZHANG²

1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, Peking University, Beijing 100871, China

收稿日期:2025-05-20 修回日期:2025-07-01 出版日期:2025-11-25 发布日期:2025-11-14

A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM

Quoc-Hung NGUYEN^1,*, Dongyi WEI², Zhifei ZHANG²

1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
2. School of Mathematical Sciences, Peking University, Beijing 100871, China

Received:2025-05-20 Revised:2025-07-01 Online:2025-11-25 Published:2025-11-14
Contact: ^*Quoc-Hung NGUYEN, E-mail: qhnguyen@amss.ac.cn
About author:Dongyi WEI, E-mail: jnwdyi@pku.edu.cn; Zhifei ZHANG, E-mail: zfzhang@math.pku.edu.cn
Supported by:
Q. H. Nguyen's research was supported by the Academy of Mathematics and Systems Science, Chinese Academy of Sciences startup fund, and the National Natural Science Foundation of China (12050410257, 12288201) and the National Key R&D Program of China (2021Y-FA1000800). He also wants to thank Alexandru Ionescu for his stimulating comments and suggestion to consider the Vlasov-Poisson system. D. Wei's research was partially supported by the National Key R&D Program of China (2021YFA1001500). Z. Zhang's research was partially supported by the NSF of China (12288101).

摘要/Abstract

摘要： This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational work of Ionescu, Pausader, Wang and Widmayer [28], we provide a streamlined proof of nonlinear Landau damping for the 3D unscreened VP system. Our analysis leverages sharp decay estimates, novel decomposition techniques to demonstrate the stabilization of the particle distribution and the decay of electric field. These results reveal the free transport-like behavior for the perturbed density $\rho(t,x)$, and enhance the understanding of Landau damping in an unconfined setting near stable equilibria.

关键词: Landau damping, Vlasov-Poisson equation, Poisson equilibrium

Abstract: This paper investigates nonlinear Landau damping in the 3D Vlasov-Poisson (VP) system. We study the asymptotic stability of the Poisson equilibrium $\mu(v)=\frac{1}{\pi^2(1+|v|^2)^2}$ under small perturbations. Building on the foundational work of Ionescu, Pausader, Wang and Widmayer [28], we provide a streamlined proof of nonlinear Landau damping for the 3D unscreened VP system. Our analysis leverages sharp decay estimates, novel decomposition techniques to demonstrate the stabilization of the particle distribution and the decay of electric field. These results reveal the free transport-like behavior for the perturbed density $\rho(t,x)$, and enhance the understanding of Landau damping in an unconfined setting near stable equilibria.

Key words: Landau damping, Vlasov-Poisson equation, Poisson equilibrium

中图分类号:

35F50

Quoc-Hung NGUYEN, Dongyi WEI, Zhifei ZHANG. A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM[J]. 数学物理学报(英文版), 2025, 45(6): 2669-2684.

Quoc-Hung NGUYEN, Dongyi WEI, Zhifei ZHANG. A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM[J]. Acta mathematica scientia,Series B, 2025, 45(6): 2669-2684.

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A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM

A NEW PROOF OF NONLINEAR LANDAU DAMPING FOR THE 3D VLASOV-POISSON SYSTEM NEAR POISSON EQUILIBRIUM

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