Exact Solutions of Unsteady Three-Dimensional Navier-Stokes Equations

New classes of exact solutions of the three-dimensional unsteady Navier Stokes equations containing arbitrary functions and parameters are discussed. A number of periodic and other solutions expressed through elementary functions were obtained and the general physical interpretation and classification of solutions was given. Self-similar, invariant, partially invariant, and certain other exact solutions of the Navier Stokes equations including those with generalized separation of variables were considered. Three-dimensional unsteady motions of a viscous incompressible fluid were described by the Navier Stokes and continuity equations. It was assumed that the mass forces were potential and included in the pressure when writing a number of these equations. The flow of a viscous incompressible fluid was also considered when the fluid-velocity vector on the z axis was directed along the same axis.