On Echo Chains in Landau damping: Self-similar Solutions and Gevrey 3 as\n a Linear Stability Threshold

2020/01/02 by Christian Zillinger, Zillinger, Christian
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Plasma Physics (physics.plasm-ph)

paper · pdf · doi:10.48550/arxiv.2001.00513

openalex publication_date 2020/01/02 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We show that the linearized Vlasov-Poisson equations around self-similar\nnon-homogeneous states near zero contain the full plasma echo mechanism,\nyielding Gevrey 3 as a critical stability class. Moreover, here Landau damping\nmay persist despite blow-up: We construct a critical Gevrey regularity class in\nwhich the force field converges in L². Thus, on the one hand, the physical\nphenomenon of Landau damping holds. On the other hand, the density diverges to\ninfinity in Sobolev regularity. Hence, ``strong damping'' cannot hold.\n

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