The Navier-Stokes Equations: On Special Classes and Properties of Exact Solutions of 3D Incompressible Flows

The global in time continuation to the three- dimensional incompressible Navier-Stokes equations remains the major unsolved problem in the mathematical fluid mechanics. This issue somehow drives qualitative mathematical analysis of the viscous incompressible flows toward the enormous development, but only a little interest pointed to the analytical methods which provide a quantitative understanding. It is discussed in the book that finding the appropriate methods for analytical treatment of the full set of incompressible Navier- Stokes equations is very important task from theoretical and practical point of view. The scope of the current investigation is to solve the three- dimensional incompressible Navier-Stokes equations and continuity equation by self developed analytical techniques which may also be applied to other equations as well. The phenomenological issue is also addressed following preliminary validating processes which are discussed in a concise manner for each case.