中文摘要：

考察三维不可压Navier-Stokes方程的弱解正则性问题.基于Holder不等式和速度场的不可压缩性质,通过对速度向量的部分分量及相关导数的估计,得到了一个新的关于Leray-Hopf弱解的正则性准则的结果.在速度向量的部分分量及相关导数满足适当的条件下,三维不可压Navier-Stokes方程的弱解是整体正则的.

英文摘要：

The global regularity problem of 3-dimensional Navier-Stokes equations was investigated.By using the Holder inequality and the divergence free condition,a regularity criterion for the 3-dimensional Navier-Stokes equations was obtained based on estimating some derivatives of the two components of the velocity.It shows that the weak solutions is global regular if some assumptions on some derivatives of the two components of the velocity were satisfied.