We prove a local-in-time regularity criterion for the 3D Navier-Stokes equations. In particular from the criterion we obtain a new partial regularity result on the dimension of possible singular times. It is shown that the Hausdorff dimension of possible singular times for weak solutions $u\in L^s([0,T]\times \mathbb{R}^3)$ with $4 \leq s \leq 5$ is at most $\frac{5}{2}-\frac{s}{2}$ improving the previous bound $\frac{1}{2}$. 查看全文>>