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I've seen the derivations for both viscous and inviscid momentum balance in fluid flow in courses, but I'm curious as to where the original derivation for the equations now referred to Euler equations or Navier-Stokes equations is. I would love to see the papers or lecture notes, even if they're in a different language.

Does anyone know what the papers are called/how to find them? I couldn't find them despite quite a bit of Googling.

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    $\begingroup$ The history of science and mathematics SE might be a better home for this question: hsm.stackexchange.com $\endgroup$ – Martin C. Jun 5 '18 at 14:29
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According to the book Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl by Olivier Darrigol, the derivation of Euler's equation by Euler and of Navier-Stokes by Stokes are essentially the modern methods: that is, one considers the balance of forces on an infinitesimal volume element. (see pages 23-25 and 135-139).

The main difference is that vector calculus notation was invented only much later, so these equations were written in a more complicated form.

You can find Euler's paper here. The paper is originally in Latin, however at that page you'll find a German translation. See also here.

You can find Stokes' paper (Trans. Camb. Phil. Soc., vol 8, pp 287-305) here.

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