A note on Constantin and Iyer's representation formula for the Navier–Stokes equations

Abstract : The purpose of this note is to establish a probabilistic representation formula for Navier–Stokes equations on a compact Riemannian manifold. To this end, we first give a geometric interpretation of Constantin and Iyer's representation formula for the Navier–Stokes equation, then extend it to a compact Riemannian manifold. We shall use Elworthy–Le Jan–Li's idea to decompose de Rham–Hodge Laplacian operator on a manifold as a sum of the square of vector fields. MSC 2010: 35Q30, 58J65 Keywords: Navier–Stokes equations, stochastic representation, de Rham–Hodge Lapla-cian, stochastic flow, pull-back vector field
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https://hal.archives-ouvertes.fr/hal-01192831
Contributor : Shizan Fang <>
Submitted on : Thursday, September 3, 2015 - 4:11:57 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Wednesday, April 26, 2017 - 2:18:58 PM

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Shizan Fang, Dejun Luo. A note on Constantin and Iyer's representation formula for the Navier–Stokes equations. 2015. ⟨hal-01192831⟩

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