True Navier–Stokes Vector PDE

Abstract

The additional equalities (additional differential equations) for the Navier - Stokes and other vector PDE are established in this paper. These equations are obligatory requirements (properties) of three functions forming a vector field on Euclidean space. Therefore all solutions of the vector PDE should satisfy these requirements. Without these equalities the Navier-Stokes equations with so called a continuity equation are underdetermined as vector system and any "exact solution" is not solution of the true Navier - Stokes vector equation.