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

Fourier solution of two-dimensional Navier Stokes equation with periodic boundary conditions and incompressible flow