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This is a continuation of our talk in March 9 about the partial

 

regularity theory for solutions to incompressible Navier-Stokes 

 

equation. Last time, we have introduced the basic notion of suitable 

 

weak solutions to the Navier-Stokes equation. We have also derived 

 

some a priori estimates for the velocity profile of a suitable weak 

 

solution to the Navier-Stokes equation. This time, we will derive a 

 

useful a priori estimate for the associated pressure of a suitable weak 

 

solution to the Navier-Stokes equation. In this talk, we will also 

 

demonstrate the way in which one can establish the famous Caffarelli-

 

Kohn-Nirenberg partial regularity theorem from these a priori 

 

estimates for a pair of suitable weak solutions to the Navier-Stokes 

 

equation.