Remarks on the Uniqueness of Weak Solutions of the Incompressible Navier–Stokes Equations

This paper studies the uniqueness of a weak solution of the incompressible Navier–Stokes Equations in the 3-dimensional case. Here the investigation is provided by using two different approaches. The first (the main) result is obtained for given functions possessing a certain smoothness, using a new approach. The other result works without additional conditions but is, in some sense, a “local” result, investigated by another approach. In addition, here the solvability and uniqueness of weak solutions to the auxiliary problems derived from the main problem are investigated.

DOI 10.1134/S1061920824030154