By multipying the Navier Stokes equations by the vector of differential
displacement and then by rearranging terms, it becomes apparent that the Navier
Stokes equations are a constraint on a vector field f constructed from algebraic
combinations of the derivatives of the fluid velocity vector v, such that the
vector f satisfies the Frobenius integrability theorem. In other words the
vector f can be expressed in terms of two independent functions at most. Using
this constraint of "two dimensionality" it is possible to derive a constraint
equation whose solution is simpler than that of the original Navier Stokes
equations. Once the constraint solution is found, the rest of the Navier Stokes
solution is found by quadratures.
