Abstract：

 

Last week, we have just established the  in time, local- property of any given ancient bounded weak solution to the incompressible Navier-Stokes equation. Today, we will discuss how to obtain higher regularity property of an ancient bounded solution. In the process, we will introduce some useful space-time embedding theorems as developed by Ladyzhenskaya and Solonnikov. If time will permit, we will introduce the more refined concept of ancient bounded mild solution to Navier-Stokes equation.