Landau Damping: Paraproducts and Gevrey Regularity

被引：27
作者：
Bedrossian J. [1 ]
Masmoudi N. [2 ]
Mouhot C. [3 ]
机构：
[1] University of Maryland, College Park
[2] Courant Institute of Mathematical Sciences, New York
[3] Centre for Mathematical Sciences, University of Cambridge, Cambridge
来源：
Annals of PDE | / 2卷 / 1期
基金：
美国国家科学基金会;
关键词：
Gevrey class; Landau damping; Nonlinear stability; Plasma physics; Vlasov equations;
D O I：
10.1007/s40818-016-0008-2
中图分类号：
学科分类号：
摘要：
We give a new, simpler, but also and most importantly more general and robust, proof of nonlinear Landau damping on Td in Gevrey-1s regularity (s> 1 / 3) which matches the regularity requirement predicted by the formal analysis of Mouhot and Villani [67]. Our proof combines in a novel way ideas from the original proof of Landau damping Mouhot and Villani [67] and the proof of inviscid damping in 2D Euler Bedrossian and Masmoudi [10]. As in Bedrossian and Masmoudi [10], we use paraproduct decompositions and controlled regularity loss along time to replace the Newton iteration scheme of Mouhot and Villani [67]. We perform time-response estimates adapted from Mouhot and Villani [67] to control the plasma echoes and couple them to energy estimates on the distribution function in the style of the work Bedrossian and Masmoudi [10]. We believe the work is an important step forward in developing a systematic theory of phase mixing in infinite dimensional Hamiltonian systems. © 2016, Springer International Publishing AG.
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