@article{4744208d5bb740fb932df96d08ea9872,
title = "PLASMA ECHOES NEAR STABLE PENROSE DATA",
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.",
keywords = "Landau damping, plasma echoes, Vlasov-Poisson",
author = "Emmanuel Grenier and Nguyen, {Toan T.} and Igor Rodnianski",
note = "Funding Information: \ast Received by the editors January 19, 2021; accepted for publication (in revised form) November 4, 2021; published electronically February 8, 2022. https://doi.org/10.1137/21M1392553 Funding: The work of the second author was partially supported by the National Science Foundation grant DMS-1764119, an AMS Centennial fellowship, and a Simons Foundation fellowship. The work of the third author was partially supported by the National Science Foundation grant DMS-1709270 and a Simons Foundation Investigator Award. \dagger CNRS et Ecole\' Normale Sup\e'rieure de Lyon, Equipe Projet Inria NUMED, INRIA Rh\{\^o}ne Alpes, Unit\e' de Math\e'matiques Pures et Appliqu\e'es, UMR 5669, 46, all\e'e d'Italie, 69364 Lyon Cedex 07, France (Emmanuel.Grenier@ens-lyon.fr). \ddagger Department of Mathematics, Penn State University, State College, PA 16803 USA (nguyen@ math.psu.edu). \S Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544 USA (irod@math.princeton.edu). 1polynomially or exponentially small, depending on the regularity of f1(v). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics.",
year = "2022",
doi = "10.1137/21M1392553",
language = "English (US)",
volume = "54",
pages = "940--953",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}