Exact solution of Navier-Stokes equations—The theory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics (II)

Abstract

This work is the continuation of the discussion of ref. [1]. In ref. [1] we applied the theory of functions of a complex variable under Dirac-Pauli representation, introduced the Kaluza “Ghost” coordinate, and turned Navier-Stokes equations of viscofluid dynamics of homogeneous and incompressible fluid into nonlinear equation with only a pair of complex unknown functions. In this paper we again combine the complex independent variable except time, and cause it to decrease in a pair to the number of complex independent variables. Lastly, we turn Navier-Stokes equations into classical Burgers equation. The Cole-Hopf transformation join up with Burgers equation and the diffusion equation is Backlund transformation in fact and the diffusion equation has the general solution as everyone knows. Thus, we obtain the exact solution of Navier-Stokes equations by Backlund transformation.