ANTONIOUK, Alexandra; ARNAUDON, Marc; CRUZEIRO, Ana Bela

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ANTONIOUK, Alexandra
Dep. Nonlinear Analysis Institute of Mathematics NAS Ukraine

ARNAUDON, Marc
Institut de Mathématiques de Bordeaux [IMB]

CRUZEIRO, Ana Bela
grupo de fisica matematica

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Article de revue

Ce document a été publié dans

Bulletin des Sciences Mathématiques. 2014-06-02, vol. 138, n° 4, p. 565-584

Elsevier

Résumé en anglais

We introduce a notion of generalized stochastic flows on manifolds, that extends to the viscous case the one defined by Brenier for perfect fluids. Their kinetic energy extends the classical kinetic energy to Brownian flows, defined as the $L^2$ norm of their drift. We prove that there exists a generalized flow which realizes the infimum of the kinetic energy among all generalized flows with prescribed initial and final configuration. We also construct generalized flows with prescribed drift and kinetic energy smaller than the $L^2$ norm of the drift. The results are actually presented for general $L^q$ norms, thus including not only the Navier-Stokes equations but also other equations such as the porous media.< Réduire

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https://oskar-bordeaux.fr/handle/20.500.12278/194625

Project ANR

/ - ANR-09-BLAN-0364

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251