Constantin and Iyer’s representation formula for the Navier–Stokes equations on manifolds – Dejun Luo (Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing)


Sala Seminari (Dip. Matematica).


In this talk, we will present 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. On a Riemannian manifold, there are several different choices of Laplacian operators acting on vector fields. 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. This is a joint work with Shizan Fang.

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