Navier-stokes equation and diffusions on the group of homeomorphisms of the torus

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.