The theory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics. I
type: Item
instance of: scholarly article
title: The theory of functions of a complex variable under Dirac-Pauli representation and its application in fluid dynamics. I
zbMATH Open document ID: 0627.76032
DOI: 10.1007/BF01898228
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1986-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 4020674
zbMATH Keywords: Dirac-Pauli representation
zbMATH Keywords: Euler's formula
author: Hui-chuan Shen
reviewed by: Lokenath Debnath
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4020674