Plasma Echoes Near Stable Penrose Data
Name
21m1392553.pdf
Description
Published version
Size
374.14 KB
Format
Adobe PDF
Checksum (MD5)
a3693e9432e55a9d007be47a55cb4908
Author(s)
Grenier, Emmanuel
Nguyen, Toan T
Rodnianski, Igor
Date Issued
February 2022
Journal
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
In this paper we construct particular solutions to the classical Vlasov--Poisson system near stable Penrose initial data on 𝕋 ×ℝ that are a combination of elementary waves with arbitrarily high frequencies. These waves mutually interact giving birth, eventually, to an infinite cascade of echoes of smaller and smaller amplitude. The echo solutions do not belong to the analytic or Gevrey classes studied by Mouhot and Villani but do, nonetheless, exhibit damping phenomena for large times.
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DOI of Published Version
https://doi.org/10.1137/21M1392553
