On uniqueness of weak solutions of incompressible Navier-Stokes equations in 3-dimensional case

TL;DR

This paper proves the uniqueness of weak solutions to the 3D incompressible Navier-Stokes equations for data in a dense subset of the usual data space, advancing understanding of solution behavior.

Contribution

It introduces a novel approach to establish uniqueness of weak solutions for a broader class of initial data in the 3D Navier-Stokes equations.

Findings

Proved uniqueness of weak solutions for data in a dense subset of the usual space.

Analyzed solvability and uniqueness of related boundary value problems.

Extended the class of initial data for which solutions are unique.

Abstract

Here we investigate 3-dimensional Navier-Stokes Equations in the incompressible case with use of different approach and we prove the uniqueness of the weak solutions for the data from the space, which is dense in usual space of data. Moreover we study the solvability and uniqueness of the weak solutions of problems associated with investigation of the main problem.