Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates

Daniel Han-Kwan; Toan T. Nguyen; Frédéric Rousset

doi:10.1007/s40818-021-00110-5

Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates

Daniel Han-Kwan, Toan T. Nguyen, Frédéric Rousset

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4 Scopus citations

Abstract

We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov–Poisson systems with screened interactions in the whole space R^d (for d≥ 3) that was first established by Bedrossian, Masmoudi and Mouhot in [5]. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in [5] (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.

Original language	English (US)
Article number	18
Journal	Annals of PDE
Volume	7
Issue number	2
DOIs	https://doi.org/10.1007/s40818-021-00110-5
State	Published - Dec 2021

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics
Geometry and Topology
Mathematical Physics
Physics and Astronomy(all)

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10.1007/s40818-021-00110-5

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title = "Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates",

abstract = "We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov–Poisson systems with screened interactions in the whole space Rd (for d≥ 3) that was first established by Bedrossian, Masmoudi and Mouhot in [5]. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in [5] (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.",

author = "Daniel Han-Kwan and Nguyen, {Toan T.} and Fr{\'e}d{\'e}ric Rousset",

note = "Funding Information: TN was partially supported by the NSF under grant DMS-1764119 and an AMS Centennial Fellowship, DHK by the grant ANR-19-CE40-0004 and FR by the grants ANR ODA and Singflows. Part of this work was done while TN was visiting Princeton University. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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AU - Rousset, Frédéric

N1 - Funding Information: TN was partially supported by the NSF under grant DMS-1764119 and an AMS Centennial Fellowship, DHK by the grant ANR-19-CE40-0004 and FR by the grants ANR ODA and Singflows. Part of this work was done while TN was visiting Princeton University. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

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N2 - We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov–Poisson systems with screened interactions in the whole space Rd (for d≥ 3) that was first established by Bedrossian, Masmoudi and Mouhot in [5]. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in [5] (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.

AB - We revisit the proof of Landau damping near stable homogenous equilibria of Vlasov–Poisson systems with screened interactions in the whole space Rd (for d≥ 3) that was first established by Bedrossian, Masmoudi and Mouhot in [5]. Our proof follows a Lagrangian approach and relies on precise pointwise in time dispersive estimates in the physical space for the linearized problem that should be of independent interest. This allows to cut down the smoothness of the initial data required in [5] (roughly, we only need Lipschitz regularity). Moreover, the time decay estimates we prove are essentially sharp, being the same as those for free transport, up to a logarithmic correction.

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Asymptotic Stability of Equilibria for Screened Vlasov–Poisson Systems via Pointwise Dispersive Estimates

Abstract

All Science Journal Classification (ASJC) codes

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