Geodesic
The second approximation of Navier–Stokes equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 718-724 
A. A. Kaspar'yants. The second approximation of Navier–Stokes equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 718-724. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a9/
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     title = {The second approximation of {Navier{\textendash}Stokes} equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Equations of motion of a viscous Newtonian fluid are derived, which, in addition to the terms of the Navier–Stokes equations, contain additional terms taking into account the relaxation effect of vorticity on the rate of strain. An independent experimental method for measuring a new parameter involved in the equations is described. As an application of the Navier–Stokes equations in the second approximation, Stokes’ hypothesis is rigorously substantiated. New similarity criteria for incompressible viscous flows are presented. The Poynting effect for viscous incompressible Newtonian fluids is theoretically explained.

[1] Sedov L. I., Mekhanika sploshnoi sredy, v. 1, Nauka, M., 1973

[2] Zhermen P., Mekhanika sploshnykh sred, Mir, M., 1965

[3] Prager V., Vvedenie v mekhaniku sploshnykh sred, Izd-vo inostr. lit., M., 1963

[4] Iamann G., Grundlagen der Bewegungslehre, Leipzig, 1905

[5] Sedov L. I., Vvedenie v mekhaniku sploshnykh sred, Fizmatgiz, M., 1962 | MR

[6] Kasparyants A. A., “Differentsialnye uravneniya vtorogo priblizheniya dlya vikhrevykh dvizhenii zhidkosti”, Zh. vychisl. matem. i matem. fiz., 7:4 (1967), 937–943

[7] Kochin N. E., Kibel I. A., Roze N. V., Teoreticheskaya gidromekhanika, v. II, Fizmatgiz, M., 1963 | Zbl

[8] Serrin Dzh., Matematicheskie osnovy klassicheskoi mekhaniki zhidkosti, Izd-vo inostr. lit., M., 1963