SAMS Subject Classification Number: 3, 26

A survey of recent results obtained in joint work with Radu Dascaliuc, Tuan Pham and Ed Waymire, relating solutions of the Navier Stokes equations of fluid mechanics to a stochastic branching process naturally associated to these equations will be presented. While the equations themselves are deterministic, the scaling properties of the equations suggest a branching structure of the Fourier transform of the equations. First noted by LeJan and Sznitman in 1997, the branching structure provides a representation of the solution provided this branching process is non explosive. Open problems remain, including the Clay foundation Millennium challenge, but simpler questions related to the structure of the branching process will be highlighted.