Geodesic
On self-similar Ovsyannikov's vortex
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 276-287.

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We study a multidimensional self-similar solution of the dynamic equations of an ideal compressible fluid. The solution describes swirling motions of a gas and is partially invariant with respect to the rotation group extended by dilations. The analysis of the solution reduces to the analysis of the singular points and manifolds of a system of fourth-order ordinary differential equations. We also give an example of a solution that describes the expansion of a swirling gas cloud into vacuum. 
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A. A. Cherevko; A. P. Chupakhin. On self-similar Ovsyannikov's vortex. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 278 (2012), pp. 276-287. http://geodesic.mathdoc.fr/item/TM_2012_278_a25/

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