On self-similar Ovsyannikov's vortex

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.