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Cipriano, F., and A. B. Cruzeiro. "Navier-stokes equation and diffusions on the group of homeomorphisms of the torus." COMMUNICATIONS IN MATHEMATICAL PHYSICS. 275 (2007): 255-269. Abstract

{A stochastic variational principle for the (two dimensional) Navier-Stokes equation is established. The velocity field can be considered as a generalized velocity of a diffusion process with values on the volume preserving diffeomorphism group of the underlying manifold. Navier-Stokes equation is reinterpreted as a perturbed equation of geodesics for the L (2) norm. The method described here should hold as well in higher dimensions.}