Navier-stokes equation and diffusions on the group of homeomorphisms of the torus

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Abstract

A stochastic variational principle for the (two dimensional) Navier-Stokes equation is established. The velocity field can be considered as a generalized velocity of a diffusion process with values on the volume preserving diffeomorphism group of the underlying manifold. Navier-Stokes equation is reinterpreted as a perturbed equation of geodesics for the L (2) norm. The method described here should hold as well in higher dimensions.
Original languageUnknown
Pages (from-to)255-269
JournalCommunications In Mathematical Physics
Volume275
Issue number1
DOIs
Publication statusPublished - 1 Jan 2007

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