  In this article the question on uniqueness of weak solution of the
incompressible Navier-Stokes Equations in the 3-dimensional case is studied.
Here the investigation is carried out with use of another approach. The
uniqueness of velocity for the considered problem is proved for given functions
from spaces that posseses some smoothness. Moreover, these spaces are dense in
respective spaces of functions, under which were proved existence of the weak
solutions. In addition here the solvability and uniqueness of the weak
solutions of auxiliary problems associated with the main problem is
investigated, and also one conditional result on uniqueness is proved.
