In this article, we study regularity criteria for the 3D micropolar fluid equations in terms of one partial derivative of the velocity. It is proved that if$$\begin{aligned} \int ^{T}_{0}\Vert \partial _{3}u\Vert ^{\frac{2}{1-r}}_{\dot{B}^{-r}_{\infty ,\infty }} dt<\infty \quad \text {with} \quad 0< r<1, \end{aligned}$$then, the solutions of the micropolar fluid equations actually are smooth on (0, T). This improves and extends many previous results.

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负正则数Besov空间中三维微极流体方程的正则性准则

在本文中，我们将根据速度的一阶导数研究3D微极性流体方程的正则性准则。证明如果$$ \ begin {aligned} \ int ^ {T} _ {0} \ Vert \ partial _ {3} u \ Vert ^ {\ frac {2} {1-r}} _ {\ dot {B} ^ {-r} _ {\ infty，\ infty}} dt <\ infty \ quad \ text {with} \ quad 0 <r <1，\ end {aligned} $$然后，微极点的解流体方程实际上在（0，T）上是平滑的 。这改善并扩展了许多以前的结果。