In the original work of Taylor and Green, a particular flow is analyzed in three spatial dimensions, with the three velocity components  at time  specified by
The continuity equation  determines that . The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step-by-step solution as time progresses.
An exact solution in two spatial dimensions is known, and is presented below.