A rigorous derivation of the Hamiltonian structure for the Vlasov equation

We consider the Vlasov equation in any spatial dimension, which has long been known [ZI76, Mor80, Gib81, MW82] to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie–Poisson type. In parallel, it is classical that the Vlasov equation is a mean-field limit for a pairwise i...

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Bibliographic Details

Published in:	Forum of Mathematics, Sigma
Main Authors:	Joseph K. Miller, Andrea R. Nahmod, Nataša Pavlović, Matthew Rosenzweig, Gigliola Staffilani
Format:	Article
Language:	English
Published:	Cambridge University Press 2023-01-01
Subjects:	35Q83 35Q70 82C05 82C22 70S05 37K06
Online Access:	https://www.cambridge.org/core/product/identifier/S2050509423000725/type/journal_article