We study the conditional regularity for the incompressible Navier–Stokes equations in the whole three-dimensional space. We show that the regularity of the flow can be achieved by controlling either the rate of change of the velocity magnitude along the streamlines or the rate of change of the kinetic energy along the streamlines. We compare our results with several results from the literature.

中文翻译：

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通过控制沿流线的速度幅度或动能的变化率，防止Navier-Stokes方程式爆裂

我们研究了整个三维空间中不可压缩Navier-Stokes方程的条件正则性。我们表明，可以通过控制沿流线的速度大小的变化率或沿流线的动能的变化率来实现流动的规律性。我们将我们的结果与文献中的一些结果进行比较。