  We study the role of the pressure in the partial regularity theory for weak
solutions of the Navier--Stokes equations. By introducing the notion of
dissipative solutions, due to Duchon \& Robert, we will provide a
generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach gives
a new enlightenment of the role of the pressure in this theory in connection to
Serrin's local regularity criterion.
