Osypchuk M. Application of vortex hydrodynamics to the problems of the formation and evolution of planetary systems

The object of the research is a new exact solution of Euler's hydrogas dynamics equations that generates a difficult vortical flow with a number of toroidal vortex rings, which was called a planetary vortex. The subject of the study is the study of the geometric, kinematic and dynamic characteristics of a planetary vortex and their application to the calculation of structures and basic parameters of star planetary systems. At implementation of dissertation work were used the methods of differential and integral calculus, methods of integration of linear and nonlinear differential equations of mathematical physics, methods of mathematical stability theory and programming in Matlab, Maple, and Mathcad and tools for constructing graphic 2D and 3D images. All theoretical results of this work and corresponding calculation models are new and have no analogues - they are compared only with modern observational data. The scientific novelty of the obtained results is that: a parametric analysis of the multi-parametric solution of hydrogas dynamics equations is simulated, which simulates the initial existence of a planetary vortex, and describes the structures of vortices and establishes the parametric conditions for bifurcation of these structures; the geometry and structures of singular points of the central dipoles of planetary vortices in the regular, singular and general cases are investigated; the characteristics of the vortices are determined; the pressure fields and pressure gradients have been studied; a numerical-analytical study of the motion of particles in the torus rings of a planetary vortex has been carried out. Due to the use of the hydrodynamic theory of cosmic phenomena, for the first time in astronomical science it has been possible to theoretically identify the full composition of new exoplanet systems in which only a few planets have been discovered. Materials of research can be used in scientific and teaching activity, and some results of the dissertation research can help astronomers-observers to more effectively search and exactly find new exoplanets around other stars.