A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem

Starting from the partial regularity results for suitable weak solutions to the Navier-Stokes Cauchy problem by Caffarelli, Kohn and Nirenberg, as a corollary, under suitable assumptions of local character on the initial data, we investigate the behavior in time of the L^1_{loc}-norm of the solution in a neighborhood of t= 0. The behavior is the same as for the resolvent operator associated to the Stokes operator.