One may question, however, whether the correction term was chosen by chance, because in a frame of reference moving with the sphere, the fluid near the sphere is almost at rest, and in that region inertial force is negligible and Stokes equation is well justified. Far away from the sphere, the flow velocity approaches u and Oseens approximation is more accurate. But Oseens equation was obtained applying the equation for the entire flow field. This question was answered by Proudman and Pearson in 1957, who solved the Navier-Stokes equations and gave an improved Stokes solution in the neighborhood of the sphere and an improved Oseen's solution at infinity, and matched the two solutions in a supposed common region of their validity. They obtained: