The Navier-Stokes Problem in Infinite Space

Abstract

This paper is devoted to the mathematical theory of the existence and uniqueness of the three dimensional Navier-Stokes solution for convergent-divergent flows. Using rotor operator and a well-known formula of vector analysis was obtained the nonlinear Volterra-Fredholm integral equation in a matrix form containing only three components of velocity vector which was solved by using the successive approximation method. Considering the pressure gradient as a potential field was determined the balance equation for defining the distribution pressure. Due to the obtained balance equation for the scalar pressure distribution were defined significant properties of the transient convergent-divergent flows with which provided a description of the constitutive relationships between three physical quantities: the velocity vector, the external and internal forces, the pressure distribution. According to the defined estimations of the velocity vector were proved the uniqueness theorems for the convergent-divergent Navier-Stokes problem in the general case.