Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes equation
type: Item
instance of: scholarly article
title: Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes equation
zbMATH Open document ID: 0998.01014
author: Olivier Darrigol
published in: Archive for History of Exact Sciences
publication date: 2002-11-25T00:00:00Z
review text: The Navier-Stokes equation, which is now considered as the universal basis of fluid mechanics, was not very influential when it was first formulated by Claude-Louis Navier in 1822. After a short look on the work of Mariotte, Euler, and d'Alembert on fluid dynamics, the author tells the complex story of this equation which was rediscovered or re-derived at least four times until 1845 by famous engineers and mathematicians: Cauchy (1823), Poisson (1829), Saint-Venant (1837), and Stokes (1845). The last chapter of the paper is devoted to the genesis of the law describing the flow of a viscous fluid through a pipe. This law, published by Gotthilf Hagen in 1839 and by Jean-Louis Poiseuille in 1841, was found empirically, on the basis of measurements. Its theoretical derivation was first given by Franz Neumann and Eduard Hagenbach in 1860 and by Emile Mathieu in 1863.
reviewed by: Andreas Kleinert
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 76-03
Mathematics Subject Classification ID: 74-03
Mathematics Subject Classification ID: 35-03
zbMATH DE Number: 1760590
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: fluid mechanics
zbMATH Keywords: Navier
zbMATH Keywords: Cauchy
zbMATH Keywords: Poisson
zbMATH Keywords: Saint-Venant
zbMATH Keywords: Stokes
zbMATH Keywords: viscous fluid
zbMATH Keywords: Hagen
zbMATH Keywords: Poiseuille
MaRDI profile type: Publication
full work available at URL: s004070200000
OpenAlex ID: W1967829438
DOI: 10.1007/S004070200000
description: scientific article; zbMATH DE number 1760590