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Between hydrodynamics and elasticity theory: The first five births of the Navier-Stokes equation. (English) Zbl 0998.01014
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.
Reviewer: A.Kleinert (Halle)

MSC:
01A55 History of mathematics in the 19th century
76-03 History of fluid mechanics
74-03 History of mechanics of deformable solids
35-03 History of partial differential equations
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