%0 Journal Article
%A Плакса, С. А.
%D 2018
%F zu2:28407
%I Axial-Symmetric Potential Flows
%J Models and Theories in Social Systems
%K Laplace Equation - Axial-symmetric potential - Stokes flow function - Streamline - Monogenic function -  Analytic function
%P 1-32
%T Metadata of the chapter that will be visualized in  SpringerLink
%U http://eprints.zu.edu.ua/28407/
%V 1
%X We consider axial-symmetric stationary flows of the ideal incompressible fluid as an important case of  potential solenoid vector fields. We establish relations between axial-symmetric potential solenoid fields  and principal extensions of complex analytic functions into a special topological vector space containing  an infinite-dimensional commutative Banach algebra. In such a way we substantiate a method for explicit  constructing axial-symmetric potentials and Stokes flow functions by means of components of the  mentioned principal extensions and establish integral expressions for axial-symmetric potentials and  Stokes flow functions in an arbitrary simply connected domain symmetric with respect to an axis. The  obtained integral expression of Stokes flow function is applied for solving boundary problem about a  streamline of the ideal incompressible fluid along an axial-symmetric body. We obtain criteria of  solvability of the problem by means distributions of sources and dipoles on the axis of symmetry and  construct unknown solutions using multipoles together with dipoles distributed on the axis.