PLASMA ECHOES NEAR STABLE PENROSE DATA

Emmanuel Grenier; Toan T. Nguyen; Igor Rodnianski

doi:10.1137/21M1392553

PLASMA ECHOES NEAR STABLE PENROSE DATA

Emmanuel Grenier, Toan T. Nguyen, Igor Rodnianski

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	940-953
Number of pages	14
Journal	SIAM Journal on Mathematical Analysis
Volume	54
Issue number	1
DOIs	https://doi.org/10.1137/21M1392553
State	Published - 2022

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Keywords

Landau damping
Vlasov-Poisson
plasma echoes

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10.1137/21M1392553

Cite this

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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, Vlasov-Poisson, plasma echoes",

author = "Emmanuel Grenier and Nguyen, {Toan T.} and Igor Rodnianski",

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year = "2022",

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AU - Grenier, Emmanuel

AU - Nguyen, Toan T.

AU - Rodnianski, Igor

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Landau damping

KW - Vlasov-Poisson

KW - plasma echoes

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

PLASMA ECHOES NEAR STABLE PENROSE DATA

Abstract

ASJC Scopus subject areas

Keywords

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