2020/09/28 by Kamal N. Soltanov, Soltanov, Kamal N.
Engineering · Mathematics · #35D30 #35K61 #35Q30 #76N10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Primary 35K55 #Secondary 76D03 #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2009.13132
openalex publication_date 2020/09/28 · openalex created_date 2020/10/01 · openalex updated_date 2026/07/28
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.