  An approximate solution to the two dimensional Navier Stokes equation with
periodic boundary conditions is obtained by representing the x any y components
of fluid velocity with complex Fourier basis vectors. The chosen space of basis
vectors is finite to allow for numerical calculations, but of variable size.
Comparisons of the resulting approximate solutions as they vary with the size
of the chosen vector space allow for extrapolation to an infinite basis vector
space. Results suggest that such a solution, with the full basis vector space
and which would give the exact solution, would fail for certain initial
velocity configurations when initial velocity and time t exceed certain limits.
