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Article Dans Une Revue Acta Mathematicae Applicatae Sinica Année : 2020

Nash Embedding, Shape Operator and Navier-Stokes Equation on a Riemannian Manifold

Shizan Fang
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Résumé

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.

Dates et versions

hal-02570891 , version 1 (12-05-2020)

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Citer

Shizan Fang. Nash Embedding, Shape Operator and Navier-Stokes Equation on a Riemannian Manifold. Acta Mathematicae Applicatae Sinica, 2020, 36 (2), pp.237-252. ⟨10.1007/s10255-020-0928-1⟩. ⟨hal-02570891⟩
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