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

TL;DR

This paper investigates the conditions under which weak solutions to the 3D incompressible Navier-Stokes equations are unique, extending previous results by employing new approaches and analyzing related problems.

Contribution

It provides a new proof of uniqueness for weak solutions in certain function spaces and explores related solvability and uniqueness issues.

Findings

Uniqueness of weak solutions proved in new function spaces

Extended the class of data for which uniqueness holds

Analyzed related boundary value problems for Navier-Stokes

Abstract

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