A certain necessary condition of potential blow up for Navier-Stokes equations

We show that a necessary condition for $T$ to be a potential blow up time is $\lim\limits_{t\uparrow T}\|v(\cdot,t)\|_{L_3}=\infty$.Comment: 16 page

Liouville theorems in unbounded domains for the time-dependent Stokes system

In this paper, We characterize bounded ancient solutions to the time-dependent Stokes system with zero boundary value in various domains, including the half space.Comment: 11 pages; final versio