The theory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics. I
This paper is concerned with the theory of complex functions under the Dirac-Pauli representation. Two examples (i) Euler's formula and (ii) Cauchy Riemann's differential equations are given to illustrate the theory. An attempt is made to simplify the Navier-Stokes equations for an incompressible viscous fluid and the equations of isentropic aerodynamics. The main theorems are: 1. The solution of the Navier-Stokes equation for an incompressible viscous fluid can be expressed in terms of the flow function \(\psi\) and its complex congregate \({\bar \psi}\) which satisfy a single equation. In particular, under certain conditions, the governing equation for \(\psi\) and \({\bar \psi}\) reduces to the equation for an incompressible planar flow. 2. The solution for a set of equations in isentropic aerodynamics can be expressed in terms of one complex unknown flow function \(\psi\) which satisfies only one equation. In the opinion of the reviewer, the solutions of the problems are incomplete. The paper contains several printing mistakes.
scientific article; zbMATH DE number 4020674
scientific article