Abstract：

 

This is a continuation of our discussion in our previous talk. This time, we will focus on the associated pressure of an ancient bounded weak solution. Since the associated pressure is related to the velocity profile in a nonlocal way via the composite of two Riesz's transforms, we have to introduce the function space of bounded mean oscillations in our treatment of the pressure term. This time, we will try to develop the full regularity in the classical sense of any bounded ancient solution to the Navier-Stokes equation.