Navier–Stokes equations, the algebraic aspect
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 397-413 Cet article a éte moissonné depuis la source Math-Net.Ru

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We present an analysis of the Navier–Stokes equations in the framework of an algebraic approach to systems of partial differential equations (the formal theory of differential equations).
Keywords: Navier–Stokes equations, integrability condition, constraints, differential algebra, symmetries, cohomology.
Mots-clés : evolution
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V. V. Zharinov. Navier–Stokes equations, the algebraic aspect. Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 397-413. http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a0/

[1] E. E. Sedov, Mekhanika sploshnoi sredy, Nauka, M., 1970 | MR | Zbl

[2] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika, v. 6, Gidrodinamika, 2001 | MR

[3] T.-P. Tsai, Lectures on Navier–Stokes Equations, Graduate Studies in Mathematics, 192, AMS, Providence, RI, 2018 | DOI | MR

[4] P. G. Lemarié-Rieusset, The Navier–Stokes Problem in the 21st Century, Chapman and Hall/CRC, Boca Raton, FL, 2016 | DOI

[5] M. V. Korobkov, K. Piletskas, V. V. Pukhnachev, R. Russo, “Zadacha protekaniya dlya uravnenii Nave–Stoksa”, UMN, 69:6(420) (2014), 115–176 | DOI | DOI | MR | Zbl

[6] C. L. Fefferman, J. C. Robinson, J. L. Rodrigo (eds.), Partial Differential Equations in Fluid Mechanics, London Mathematical Society Lecture Note Series, 452, Cambridge Univ. Press, Cambridge, 2018 | DOI

[7] W. M. Seiler, Involution: The Formal Theory of Differential Equations and its Applications in Computer Algebra, Algorithms and Computation in Mathematics, 24, Springer, Berlin–Heidelberg, 2010 | DOI

[8] P. Olver, Prilozhenie grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | DOI | MR | Zbl

[9] S. Maklein, Gomologiya, Mir, M., 1966 | DOI | MR | Zbl

[10] V. V. Zharinov, “Zakony sokhraneniya evolyutsionnykh sistem”, TMF, 68:2 (1986), 163–171 | DOI | MR | Zbl

[11] V. V. Zharinov, “Zakony sokhraneniya, differentsialnye tozhdestva i svyazi uravnenii v chastnykh proizvodnykh”, TMF, 185:2 (2015), 227–251 | DOI | DOI | MR