What year were Navier-Stokes equations introduced?

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user079622
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Who and when first time introduced below equations(dont have to be in same notation, content is important)?

0bZdvG1C.jpg



If this formula is always the same, what is contribution of Navier, what of Stokes, what changes all these years?
 
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Between Navier in 1821-2 and Stokes report in 1846, many mathematicians and experimenters were trying to find a more tractable solution. The names dropped by Stokes in his 1846 discussion and summary of that period include; Airy, Cauchy, Challis, Coulomb, Dubuat, Girard, Green, Kelland, Lagrange, Navier, Ostrogradsky, Plana, Poisson, Power, and Russel.

Those attempts involved changing assumptions like the shape of the fluid parcel between square, tetrahedral, sphere and ellipsoid, considering compressibility or not, and how to handle circulation, while investigating viscosity and understanding the boundary layer.

It seems many wanted to avoid Navier's intractable equations, but a better alternative was not found.
 
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I find this:

http://physics.uwyo.edu/~rudim/ArchHistExSci56_2002_FiveBirthsOfNavierStokes_Sum15.pdf

"Éléments d’analyse
des articles historiques
de Navier
La contribution historique de Navier aux équations du mouvement des flui-des a fait l’objet d’une présentation à l’Académie des sciences le 18 mars 1822, et se trouve développée dans deux contributions écrites :
– « Sur les lois des mouvements des fluides, en ayant égard à l’adhésion des molécules », Annales de chimie et de physique, tome XIX, 1821 ;
– « Sur les lois des mouvements des fluides » (lu à l’Académie des sciences le 18 mars 1822), Mémoires de l’Académie des sciences, sciences mathématiques et physiques, tome VI (1823), 1827.

L’article de 1821, que l’on peut consi-dérer comme article fondateur, secontente de développer les conséquen-ces de l’hypothèse sur l’expression locale de la force de viscosité (il ren-voie d’ailleurs pour les détails à une autre contribution récente de Navier, elle aussi de 1821, relative aux lois de l’élasticité, qui contient une mise en équations et un calcul formellement semblables), puis injecte cette force supplémentaire dans les équations d’Euler."
 

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Baluncore said:
"On the development of the Navier-Stokes equation by Navier"
For the notation used by Navier see:
https://www.scielo.br/j/rbef/a/nNpqpRmKN8J3zPhV4WN4vFF/?lang=en#
Look at section 4 of this text.

My copy of the .pdf came from:
https://www.scielo.br/j/rbef/a/nNpqpRmKN8J3zPhV4WN4vFF/?format=pdf&lang=en
What are differences in equations from https://gallica.bnf.fr/ark:/12148/bpt6k6571078m/f250.item and https://perso.crans.org/epalle/M2/EC/Histoire/Navier1822MemoireSurLesLoisDuMouvementDesFluides.pdf?
 
berkeman said:
Why don't you read the papers and tell us?
Because I dont understand France and cartesian hieroglyphics.
 
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user079622 said:
Because I dont understand France and cartesian hieroglyphics.
You are asking too much of others to do your work for you. Thread is closed.