Symmetry reduction and exact solutions of the Navier-Stokes equations
  Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the Navier-Stokes equations to system of differential equations in three, two, and one independent variables. The large sets of exact solutions of the Navier-Stokes equations are constructed. 
Wilhelm I. Fushchych and Roman O. Popovych