Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively simple scale-invariant relation involving 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 different treatments leading to essentially the same conclusion are presented.

翻译：考虑到整个空间的三维不可压缩纳维埃-斯托克斯方程式,我们处理的问题是:从一个单一的近似解决方案推断出一个温度解决方案是否具有全球规律性?假设一个相对简单的比例-差异关系,涉及近似解决方案的大小、分辨率参数和初始能量,我们表明答案是肯定的,包括Leray的软化解决方案。提出了两种不同处理方法,得出基本相同的结论。