Constantin and Iyer’s representation formula for the Navier–Stokes equations on manifolds - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Potential Analysis Année : 2018

Constantin and Iyer’s representation formula for the Navier–Stokes equations on manifolds

Résumé

The purpose of this paper is to establish a probabilistic representation formula for the Navier--Stokes equations on compact Riemannian manifolds. Such a formula has been provided by Constantin and Iyer in the flat case of $\mathbb R^n$ or of $\mathbb T^n$. On a Riemannian manifold, however, there are several different choices of Laplacian operators acting on vector fields. In this paper, we shall use the de Rham--Hodge Laplacian operator which seems more relevant to the probabilistic setting, and adopt Elworthy--Le Jan--Li's idea to decompose it as a sum of the square of Lie derivatives.

Dates et versions

hal-01701332 , version 1 (05-02-2018)

Identifiants

Citer

Shizan Fang, Dejun Luo. Constantin and Iyer’s representation formula for the Navier–Stokes equations on manifolds. Potential Analysis, 2018, 48 (2), pp.181-206. ⟨10.1007/s11118-017-9631-0⟩. ⟨hal-01701332⟩
67 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More