Singular solutions for geodesic flows of Vlasov moments

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Title: Singular solutions for geodesic flows of Vlasov moments
Authors: Gibbons, J
Holm, DD
Tronci, C
Item Type: Working Paper
Abstract: The Vlasov equation for the collisionless evolution of the single-particle probability distribution function (PDF) is a well-known example of coadjoint motion. Remarkably, the property of coadjoint motion survives the process of taking moments. That is, the evolution of the moments of the Vlasov PDF is also coadjoint motion. We find that {\it geodesic} coadjoint motion of the Vlasov moments with respect to powers of the single-particle momentum admits singular (weak) solutions concentrated on embedded subspaces of physical space. The motion and interactions of these embedded subspaces are governed by canonical Hamiltonian equations for their geodesic evolution.
Issue Date: 28-Mar-2006
URI: http://hdl.handle.net/10044/1/72624
Copyright Statement: © 2006 The Authors.
Keywords: nlin.CD
nlin.CD
nlin.PS
nlin.CD
nlin.CD
nlin.PS
Notes: 20 pages, no figures
Publication Status: Published
Open Access location: http://library.msri.org/books/Book55/files/09holm.pdf
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics



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