  This is largely an attempt to provide probabilists some orientation to an
important class of non-linear partial differential equations in applied
mathematics, the incompressible Navier-Stokes equations. Particular focus is
given to the probabilistic framework introduced by LeJan and Sznitman [Probab.
Theory Related Fields 109 (1997) 343-366] and extended by Bhattacharya et al.
[Trans. Amer. Math. Soc. 355 (2003) 5003-5040; IMA Vol. Math. Appl., vol. 140,
2004, in press]. In particular this is an effort to provide some foundational
facts about these equations and an overview of some recent results with an
indication of some new directions for probabilistic consideration.
