Spherically symmetric stationary flows of a rarefied two-phase fluid

The spherically symmetric stationary flows of isothermal rarefied two-phase fluid are studied. The results of the research give a qualitative description such flows for arbitrary positive initial data. Namely, for arbitrary positive initial velocities and densities of the first and the second phase, which are set at the initial sphere of arbitrary radius, the obtained phase portrait gives a qualitative description of the distribution of characteristics at the spheres of other radii. A classification of all possible types of spherically symmetric stationary flows of isothermal two-phase fluid in a case of the spread of a substance has been carried out. In the work it is also described a bifurcation of a dynamical system. As a result of this bifurcation, some attracting set appears at the curve of singular points. The emergence of this set greatly changes a quantity of the types of two-phase flows. Another result of the study is a description of all types of continuous transonic spherically symmetric stationary flows at the investigating model of two-phase fluid. The study showed that if the ratio of the flows of the first and second phases through an initial sphere is bigger than 8, then there is a non-zero probability of a realization in two-phase fluid dynamics a continuous transition from supersonic mode to subsonic mode. There have been carried out different numerical experiments, which are illustrated the obtained results.