Abstract
In this article the Navier - Stokes (NSE) exact transformations to the simpler equations is covered. This transformation is executed by classical methods of Mathematical Analysis. The solution of such equations is simpler than solution of the well known NSE. These new equations essentially facilitate the solutions of the Navier - Stokes Millennium Problem and different problems of numerous applications of Applied Mathematics in engineering.
Highlights
The Navier–Stokes equations (NSE) in the case of incompressible flow are given by ρF − grad p + μ∇2u = ρu
The aim of this paper is to prove that the NSE exact transformation to the simpler equations is possible
These new equations should facilitate the solution of Navier–Stokes existence and smoothness one of seven Millennium Prize Problems that were stated by the Clay Mathematics Institute
Summary
The Navier–Stokes equations (NSE) in the case of incompressible flow are given by ρF − grad p + μ∇2u = ρu (1). The aim of this paper is to prove that the NSE exact transformation to the simpler equations is possible. These new equations should facilitate the solution of Navier–Stokes existence and smoothness one of seven Millennium Prize Problems that were stated by the Clay Mathematics Institute. New equations will simplify the solutions of many problems of Applied Mathematics in engineering. With such equation is called a continuity equation (if ρ =Const ) [1, p. For incompressible flow if the continuity equation is equivalent to dρ dt =∂ρ ∂t + u x ∂ρ ∂x
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