A new method for obtaining the exact solutions of the Navier-Stokes (NS) equations and its applications

Abstract

In this paper we propose a new method for obtaining the exact solutions of the Mavier-Stokes (NS) equations for incompressible viscous fluid in the light of the theory of simplified Navier-Stokes (SNS) equations developed by the first author[1,2], Using the present method we can find some new exact solutions as well as the well-known exact solutions of the NS equations. In illustration of its applications, we give a variety of exact solutions of incompressible viscous fluid flows for which NS equations of fluid motion are written in Cartesian coordinates, or in cylindrical polar coordinates, or in spherical coordinates.