A global regularity criterion for the Navier-Stokes equations based on approximate solutions

10/12/2019

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by   Tuan Pham, et al.

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We address the following question: is it possible to infer global regularity of mild solution from a single approximate solution? Assuming a relatively simple scale-invariant relation of the size of the approximate solution, the resolution parameter, and the initial energy, we show that the answer is affirmative for a general class of approximate solutions, including Leray's mollified solutions. Two treatments leading to essentially the same conclusion are presented.