The First Integral Method for the Two-dimensional Incompressible Navier-Stokes Equations

In this paper, we deal with the first integral method to find exact solutions for The Two-Dimensional Incompressible Navier-Stokes equations. This method is an algebraic direct method used division theorem to find the first integral through polynomial and use traveling wave solution to transform the partial differential equation into the ordinary differential equation. We get different exact solutions through the use of this method and these solutions are either of the formula of exponential, hyperbolic or trigonometric functions.