  The Navier-Stokes equations, which govern fluid motions, are not resolved
yet. This investigation relates to the application of the power series method
to the incompressible Navier-Stokes equations. This method involves replacing
variables by power series in the equations. The resulting relations allow the
computation of the series coefficients from the initial and boundary
conditions. All the steps of applying the method to the Navier-Stokes equations
are detailed and the exact analytical solution is then established. The last
part discusses the domain of convergence of the solution.
