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Considering the three-dimensional incompressible Navier-Stokes equations onthe whole space, we address the question: is it possible to infer globalregularity of a mild solution from a single approximate solution? Assuming arelatively simple scale-invariant relation involving the size of theapproximate solution, the resolution parameter, and the initial energy, we showthat the answer is affirmative for a general class of approximate solutions,including Leray's mollified solutions. Two different treatments leading toessentially the same conclusion are presented.

Global regularity criteria for the Navier-Stokes equations based on one approximate solution