Geodesic
Some solutions of the Euler system of an inviscid incompressible fluid
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 672-678 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a system of two-dimensional Euler equations describing the motions of an inviscid incompressible fluid. It reduces to one non-linear equation with partial derivatives of the third order. A group of point transformations allowed by this equation is found. Some invariant solutions and solutions not related to invariance are constructed. The solutions found describe vortices, jet streams, and vortex-like formations.
Keywords: vortices
Mots-clés : Euler equations, group of point transformations, invariant solutions, jets. 
@article{JSFU_2022_15_5_a14,
     author = {Oleg V. Kaptsov},
     title = {Some solutions of the {Euler} system of an inviscid incompressible fluid},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {672--678},
     year = {2022},
     volume = {15},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a14/}
}
TY  - JOUR
AU  - Oleg V. Kaptsov
TI  - Some solutions of the Euler system of an inviscid incompressible fluid
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 672
EP  - 678
VL  - 15
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a14/
LA  - en
ID  - JSFU_2022_15_5_a14
ER  - 
%0 Journal Article
%A Oleg V. Kaptsov
%T Some solutions of the Euler system of an inviscid incompressible fluid
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 672-678
%V 15
%N 5
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a14/
%G en
%F JSFU_2022_15_5_a14
Oleg V. Kaptsov. Some solutions of the Euler system of an inviscid incompressible fluid. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 5, pp. 672-678. http://geodesic.mathdoc.fr/item/JSFU_2022_15_5_a14/

[1] G. Batchelor, An introduction to fluid dynamics, Cambridge University Press, 1970 | MR

[2] V. Andreev, O. Kaptsov, V. Pukhnachov, A. Rodionov, Applications of group-theoretical methods in hydrodynamics, Kluwer Academic Publishers, 1998 | MR | Zbl

[3] A.A. Abrashkin, E.I. Yakubovich, Vortex Dynamics in Lagrangian Description, FIZMATLIT, M., 2006 (in Russian)

[4] L. Woods, Theory of Tokamak Transport. New Aspects for Nuclear Fusion Reactor Design, Wiley-VCH, Weinheim, 2006 | Zbl

[5] L.V. Ovsyannikov, Group Analysis of Differential Equations, Academic Press, NY, 1982 | MR | Zbl

[6] Yu.V. Shan'ko, “Exact solutions of axially symmetric Euler equations”, Appl. Maths Mech., 60:3 (1996), 433–437 | DOI | MR