Generalized Navier-Stokes flows

Marc Arnaudon (1) , Ana Bela Cruzeiro (2)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]
2 Departamento de Matemática IST (TUL) and GFMUL

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.

Mots clés: Navier-Stokes equation; generalized stochastic flows; stochastic variational principle

Domaines: Probabilités [math.PR]

Marc Arnaudon, Ana Bela Cruzeiro. Generalized Navier-Stokes flows. 2012. ⟨hal-00702509⟩