Splitting method and the existence of a strong solution of the Navier-Stokes equations

Abstract

In the author’s article from the previous issue of the journal from the properties of the ONS solutions the relation between pressure and module square of velocity vector is set. Based on which the uniqueness of the weak and existence of strong solutions of the problem for three - dimensional equations of Navier-Stokes as a whole over time are proved. The result is a contribution to a qualitative mathematical theory of the NavierStokes equations. However, one of the actual problems in the theory of equations of Navier - Stokes is the choice of the mathematical method for proofs of the existence of a theorem. In the work splitting method is chosen to solve the Navier-Stokes equations. The rationale of this method is given. The compactness of the solution sequence is showed, thus the existence of strong solutions of the problem for three - dimensional Navier-Stokes equations as a whole over time is proved.