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

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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 
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/
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