In the domain , the solution is given by
where ,  being the kinematic viscosity of the fluid. Following the analysis of Taylor and Green for the two-dimensional situation, and for , gives agreement with this exact solution, if the exponential is expanded as a Taylor series, i.e. .
The pressure field  can be obtained by substituting the velocity solution in the momentum equations and is given by
The stream function of the Taylor–Green vortex solution, i.e. which satisfies  for flow velocity , is
Similarly, the vorticity, which satisfies , is given by
The Taylor–Green vortex solution may be used for testing and validation of temporal accuracy of Navier–Stokes algorithms.
A generalization of the Taylor–Green vortex solution in three dimensions in described in.