A stochastic Lagrangian representation of the 3d incompressible NavierStokes equations

Abstract. In this paper we derive a representation of the deterministic 3-dimensional Navier-Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self-contained proof of local existence for the nonlinear stochastic system, and can be extended to formulate stochas-tic representations of related hydrodynamic-type equations, including viscous Burgers equations and LANS-alpha models. 1