Generalized stochastic Lagrangian paths for the Navier-Stokes equation
Résumé
The purpose of this work is to establish a counterpart for the Navier-Stokes equation of Brenier's generalized flows for the Euler equation. We introduce a class of semi-martingales on a compact Riemannian manifold which will be generalized solutions of the Navier-Stokes equation. We prove that these semimartingales are critical points to the corresponding kinetic energy and that classical solutions of the Navier-Stokes equation realize the minimum of the kinetic energy in a suitable class.
Domaines
Probabilités [math.PR]Origine | Fichiers produits par l'(les) auteur(s) |
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