  In this article we study the uniqueness of the weak solution of the
incompressible Navier-Stokes Equation in the 3-dimensional case with use of
different approach. Here the uniqueness of the obtained by Leray of the weak
solution is proved in the case, when datums from spaces that are densely
contained into spaces of datums for which was proved the existence of the weak
solution. Moreover we investigate the solvability and uniqueness of the weak
solutions of problems associated with investigation of the main problem
