Geodesics in the Space of Measure-Preserving Maps and Plans View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2009-11

AUTHORS

Luigi Ambrosio, Alessio Figalli

ABSTRACT

We study Brenier’s variational models for incompressible Euler equations. These models give rise to a relaxation of the Arnold distance in the space of measure-preserving maps and, more generally, measure-preserving plans. We analyze the properties of the relaxed distance, we show a close link between the Lagrangian and the Eulerian model, and we derive necessary and sufficient optimality conditions for minimizers. These conditions take into account a modified Lagrangian induced by the pressure field. Moreover, adapting some ideas of Shnirelman, we show that, even for non-deterministic final conditions, generalized flows can be approximated in energy by flows associated to measure-preserving maps. More... »

PAGES

421-462

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-008-0189-2

DOI

http://dx.doi.org/10.1007/s00205-008-0189-2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1005632696


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