CKN theory of singularities of weak solutions of the Navier-Stokes equations

The lectures are devoted to a complete exposition of the theory of singularities of the Navier Stokes equations solution studied by Leray, in a simple geometrical setting in which the fluid is enclosed in a container $\O$ with periodic boundary conditions and side size $L$. The theory is due to the work of Scheffer, Caffarelli, Kohn, Nirenberg and is called here CKN-theory as it is inspired by the work of the last three authors which considerably improved the earlier estimates of Scheffer.