The natural solvability of the Navier-Stokes equations

Abstract

It is known that the three-dimensional Navier-Stokes equations (ЕNS) the existence theorem of smooth solutions in the presence of smooth data for the whole with respect to time has not proved and the uniqueness theorem is violated in the class of generalized solutions. In a number of works by the author of this article, the results of search studies on the justification of the maximum principle for three-dimensional ЕNS are given. Over time, these studies have improved and later the justice of the simplest principle for maximum was shown for three-dimensional ЕNS. A further continuation of the search led to the determination of the relationship between pressure and the square of the velocity vector modulus from the properties of the ЕNS solutions. On the basis of this the answers to many problematic issues related to the solvability of the ЕNS were found. And in particular, in the selected spaces, the uniqueness of the weak and the existence of strong solutions of the problem for the three-dimensional Navier-Stokes equations for the whole of time are proved.