中文摘要：

在Besov空间中研究三维广义Navier-Stokes方程弱解的正则性准则.利用Besov空间的对数型不等式,获得了一个关于速度场梯度的正则性准则,证明了当速度场在Besov空间中满足一定的临界增长条件时,方程的弱解实际上是存在区间上的强解.

英文摘要：

In this paper,the regularity criterion for the 3D generalised Navier-stokes equations in Besov space was studied.A regularity criterion on the gradient of velocity was obtained by the method of the inequalities in the Besov space with the logarithmic form.The result suggested the weak solution was actually strong solution if velocity field satisfies some growth condition in Besov space.