  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{equation*}
\int^{T}_{0}\|\partial_{3}u\|^{\frac{2}{1-r}}_{\dot{B}^{-r}_{\infty,\infty}}
dt<\infty \quad \text{with} \quad 0< r<1, \end{equation*} then, the solutions
of the micropolar fluid equations actually are smooth on $(0, T)$. This
improves and extends many previous results.
