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Axial-Symmetric Potential Flows

  • S. A. Plaksa
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 179)

Abstract

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.

Keywords

Laplace Equation Axial-symmetric potential Stokes flow function Streamline Monogenic function Analytic function 

Notes

Acknowledgements

This research is partially supported by Grant of Ministry of Education and Science of Ukraine (Project No. 0116U001528).

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Authors and Affiliations

  1. 1.Department of Complex Analysis and Potential TheoryInstitute of Mathematics of the National Academy of Science of UkraineKyivUkraine

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