21746 articles – 15574 references  [version française]

hal-00702509, version 1

Generalized Navier-Stokes flows

Marc Arnaudon () 1, Ana Bela Cruzeiro 2

(2012-05-30)

Abstract: We introduce a notion of generalized Navier-Stokes flows on manifolds, that extends to the viscous case the one defined by Brenier. Their kinetic energy extends the kinetic energy for classical Brownian flows, defined as the L2 norm of their drift. We prove that there exists a generalized flow which realizes the infimum of kinetic energies among all generalized flows with prescribed initial and final configuration. Finally we construct generalized flows with prescribed drift and kinetic energy smaller than the L2 norm of the drift.

  • 1:  Laboratoire de Mathématiques et Applications (LMA-Poitiers)
  • CNRS : UMR6086 – Université de Poitiers
  • 2:  Grupo de Física Matemática - Group of Mathematical Physics (GFM)
  • Universidade de Lisboa
  • Domain : Mathematics/Probability
  • Keywords : Navier-Stokes equation – generalized stochastic flows – stochastic variational principle
 
  • hal-00702509, version 1
  • http://hal.archives-ouvertes.fr/hal-00702509
  • oai:hal.archives-ouvertes.fr:hal-00702509
  • From: Ana Bela Cruzeiro <>
  • Submitted on: Wednesday, 30 May 2012 14:29:01
  • Updated on: Wednesday, 30 May 2012 15:20:26