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

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

11 Citations (Scopus)

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	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
Publication status	Published - 2022
Externally published	Yes

Keywords

Landau damping
Vlasov-Poisson
plasma echoes

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10.1137/21M1392553

Cite this

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

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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

UR - https://www.scopus.com/pages/publications/85128932458

U2 - 10.1137/21M1392553

DO - 10.1137/21M1392553

M3 - Article

AN - SCOPUS:85128932458

SN - 0036-1410

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EP - 953

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

PLASMA ECHOES NEAR STABLE PENROSE DATA

Abstract

Keywords

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