On the uniqueness of a suitable weak solution to the Navier–Stokes Cauchy problem

The paper is concerned with the Navier–Stokes Cauchy problem. We investigate on some results of regularity and uniqueness related to suitable weak solutions corresponding to a special set of initial data. The suitable weak solution notion is meant in the sense introduced by Caffarelli–Kohn–Nirenberg.As further result we discuss the uniqueness of a set of suitable weak solutions (wider than the previous one) enjoying a “Prodi–Serrin” condition which is “relaxed” in space.