Navier–Stokes equations, the algebraic aspect
Teoretičeskaâ i matematičeskaâ fizika, Tome 209 (2021) no. 3, pp. 397-413

Voir la notice de l'article provenant de la source Math-Net.Ru

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
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/
@article{TMF_2021_209_3_a0,
     author = {V. V. Zharinov},
     title = {Navier{\textendash}Stokes equations, the~algebraic aspect},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {397--413},
     year = {2021},
     volume = {209},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a0/}
}
TY  - JOUR
AU  - V. V. Zharinov
TI  - Navier–Stokes equations, the algebraic aspect
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2021
SP  - 397
EP  - 413
VL  - 209
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a0/
LA  - ru
ID  - TMF_2021_209_3_a0
ER  - 
%0 Journal Article
%A V. V. Zharinov
%T Navier–Stokes equations, the algebraic aspect
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2021
%P 397-413
%V 209
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2021_209_3_a0/
%G ru
%F 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