Geodesic
Stationary Ovsyannikov vortex in the field of large gravitating center
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 2, pp. 228-243.

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

The three-dimensional motion of gas within the limits of model of a stationary special vortex with gravitation is considered. Using methods of the group analysis of the differential equations, it is possible to reduce studying of properties of the decision to research of properties of an implicitly defined ordinary differential equation. The properties of solutions of this equation are studied, a description of modes of a current in the phase space is obtained, the existence of subsonic and supersonic modes of a gas motion in physical space is proved. It is shown that classification of types of decisions and their qualitative behavior to a similar case of a vortex of Ovsyannikov without gravitation (A. A. Cherevko, A. P. Chupakhin, 2005).
Mots-clés : Ovsyannikov vortex, jet space.
Keywords: group analysis of differential equations, implicit differential equation 
@article{JSFU_2010_3_2_a8,
     author = {Daniil V. Parshin and Alexander P. Chupakhin},
     title = {Stationary {Ovsyannikov} vortex in the field of large gravitating center},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {228--243},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2010_3_2_a8/}
}
TY  - JOUR
AU  - Daniil V. Parshin
AU  - Alexander P. Chupakhin
TI  - Stationary Ovsyannikov vortex in the field of large gravitating center
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2010
SP  - 228
EP  - 243
VL  - 3
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2010_3_2_a8/
LA  - ru
ID  - JSFU_2010_3_2_a8
ER  - 
%0 Journal Article
%A Daniil V. Parshin
%A Alexander P. Chupakhin
%T Stationary Ovsyannikov vortex in the field of large gravitating center
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2010
%P 228-243
%V 3
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2010_3_2_a8/
%G ru
%F JSFU_2010_3_2_a8
Daniil V. Parshin; Alexander P. Chupakhin. Stationary Ovsyannikov vortex in the field of large gravitating center. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 2, pp. 228-243. http://geodesic.mathdoc.fr/item/JSFU_2010_3_2_a8/

[1] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[2] L. I. Sedov, Metody podobiya i razmernosti v mekhanike, Nauka, M., 1981 | MR | Zbl

[3] K. P. Stanyukovich, Neustanovivshiesya dvizheniya sploshnoi sredy, Nauka, M., 1971 | MR

[4] L. V. Ovsyannikov, “Osobyi vikhr”, PMTF, 36:3 (1995), 45–52 | MR | Zbl

[5] A. A. Cherevko, A. P. Chupakhin, Statsionarnyi vikhr Ovsyannikova, Preprint IGiL No 1, 2005

[6] V. I. Arnold, Geometricheskie metody v teorii obyknovennykh differentsialnykh uravnenii, Izhevskaya respublikanskaya tipografiya, Izhevsk, 2002

[7] A. S. Pavlenko, “Proektivnaya podmodel vikhrya Ovsyannikova”, PMTF, 46:4 (2005), 3–16 | MR | Zbl