摘要
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.
