"The mathematical theory of the Navier-Stokes equations has centered upon basic questions of the existence, uniqueness, and regularity of solutions of the initial value problem for fluid motions in all of space or in a subdomain of finite or infinite extent. Such solutions, when they can be constructed or shown to exist, represent flows of a viscous incompressible fluid. In two space dimensions the theorem of existence, uniqueness and regularity was essentially completed thirty years ago by the work of Leray ..., Lions ... and Ladyzhenskaya ... who showed that a smooth solution of the initial value problem exists for arbitrary square-integrable initial data. For viscous, incompressible fluid motions in three space dimensions, ... the theorem of existence uniqueness and regularity has been proved only for sufficiently small initial data or in special cases such as cylindrical symmetry that essentially reduce the problem to two space dimensions in some sense."