In this paper, we are concerned with the regularity of suitable weak solutions to the 3D Navier–Stokes equations in Lorentz spaces. We obtain \(\varepsilon \)-regularity criteria in terms of either the velocity, the gradient of the velocity, the vorticity or deformation tensor in Lorentz spaces, which generalizes the corresponding results derived by Gustafson et al. (Commun Math Phys 273:161–176, 2007) in Lebesgue spaces. As applications, this allows us to extend recent results involving Leray’s blow up rate in time, and to show that the number of singular points of weak solutions belonging to \( L^{p,\infty }(-1,0;L^{q,l}({\mathbb {R}}^{3})) \) is finite, where the pair (p, q) satisfies \( {2}/{p}+{3}/{q}=1\) with \(3<q<\infty \) and \(q\le l <\infty \).

在本文中，我们关注3维Navier–Stokes方程在Lorentz空间中合适的弱解的正则性。我们根据Lorentz空间中的速度，速度梯度，涡度或形变张量获得\（\ varepsilon \） -正则性标准，从而推广了Gustafson等人得出的相应结果。（Commun Math Phys 273：161–176，2007）在Lebesgue空间中。作为应用，这使我们能够及时扩展涉及Leray爆炸率的最新结果，并证明弱解的奇异点数属于\（L ^ {p，\ infty}（-1,0; L ^ {q，l}（{\ mathbb {R}} ^ {3}））\）是有限的，其中对（p，  q）满足\（{2} / {p} + {3} / {q} = 1 \）与\（3 <q <\ infty \）和\（q \ le l <\ infty \）。