Instabilities in the Mean Field Limit

Daniel Han-Kwan; Toan T. Nguyen

doi:10.1007/s10955-016-1455-6

Instabilities in the Mean Field Limit

Daniel Han-Kwan
, Toan T. Nguyen

École Polytechnique

Pennsylvania State University

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

6 Citations (Scopus)

Abstract

Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.

Original language	English
Pages (from-to)	1639-1653
Number of pages	15
Journal	Journal of Statistical Physics
Volume	162
Issue number	6
DOIs	https://doi.org/10.1007/s10955-016-1455-6
Publication status	Published - 1 Mar 2016

Keywords

Instability
Mean field limit
Vlasov
Wasserstein distance

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10.1007/s10955-016-1455-6

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title = "Instabilities in the Mean Field Limit",

abstract = "Consider a system of N particles interacting through Newton{\textquoteright}s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.",

keywords = "Instability, Mean field limit, Vlasov, Wasserstein distance",

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T1 - Instabilities in the Mean Field Limit

AU - Han-Kwan, Daniel

AU - Nguyen, Toan T.

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N2 - Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.

AB - Consider a system of N particles interacting through Newton’s second law with Coulomb interaction potential in one spatial dimension or a (Formula presented.) smooth potential in any dimension. We prove that in the mean field limit (Formula presented.) , the N particles system displays instabilities in times of order (Formula presented.) , for some configurations approximately distributed according to unstable homogeneous equilibria.

KW - Instability

KW - Mean field limit

KW - Vlasov

KW - Wasserstein distance

U2 - 10.1007/s10955-016-1455-6

DO - 10.1007/s10955-016-1455-6

M3 - Article

AN - SCOPUS:84959136766

SN - 0022-4715

VL - 162

SP - 1639

EP - 1653

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 6

ER -

Instabilities in the Mean Field Limit

Abstract

Keywords

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