Nash embedding, shape operator and Navier-Stokes equation on a Riemannian manifold

Abstract : What is the suitable Laplace operator on vector fields for the Navier-Stokes equation on a Riemannian manifold? In this note, by considering Nash embedding, we will try to elucidate different aspects of different Laplace operators such as de Rham-Hodge Laplacian as well as Ebin-Marsden's Laplacian. A probabilistic representation formula for Navier-Stokes equations on a general compact Riemannian manifold is obtained when de Rham-Hodge Laplacian is involved. MSC 2010: 35Q30, 58J65
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Contributor : Shizan Fang <>
Submitted on : Sunday, July 28, 2019 - 6:46:24 PM
Last modification on : Tuesday, July 30, 2019 - 1:23:18 AM

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  • HAL Id : hal-02196468, version 1
  • ARXIV : 1907.13519

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Shizan Fang. Nash embedding, shape operator and Navier-Stokes equation on a Riemannian manifold. 2019. ⟨hal-02196468⟩

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