In this paper, we provide a regularity criterion for 3D Navier–Stokes equations in terms of two vorticity components, which extends a recent result established by Guo, Kučera and Skalák (2018). More precisely, we prove that a unique local strong solution $u$ to 3D Navier–Stokes equations does not blow up at time $T$ provided only two components of vorticity belongs to $L^2(0,T;BM{O}^{-1})$. We also prove that $u$ can be smoothly extended beyond $T$, if the horizontal gradient of horizontal components of velocity $u$ belong to $L^2(0,T;BM{O}^{-1})$. The proof relies on the technique of the Bony decomposition and some Fourier multiplier theorems.

在本文中，我们根据两个涡度分量提供了3D Navier-Stokes方程的正则性准则，扩展了Guo，Kučera和Skalák（2018）建立的最新结果。更确切地说，我们证明了独特的本地强大解决方案$ü$ 到3D Navier–Stokes方程式时不会爆炸 $Ť$ 只要涡度的两个分量属于 ${\mathrm{大号}}^2（0，Ť;乙\mathrm{中号}{Ø}^{-\mathrm{1个}}）$。我们还证明$ü$ 可以顺利扩展到 $Ť$，如果速度的水平分量的水平梯度 $ü$ 属于 ${\mathrm{大号}}^2（0，Ť;乙\mathrm{中号}{Ø}^{-\mathrm{1个}}）$。证明依赖于Bony分解技术和一些傅立叶乘子定理。