Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus

We establish a connection between the strong solution to the spatially periodic Navier-Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on the group of diffeomorphisms of a flat torus. We construct a representation of the strong solution to the Navier-Stokes equations in terms of diffusion processes (joint work with A. B. Cruzeiro).