Abstract
We obtain a new representation of potential and flow functions for space potential solenoidal fields with axial symmetry. We study principal algebraic-analytical properties of monogenic functions of a vector variable with values in an infinite-dimensional Banach algebra of even Fourier series and describe the relationship between these functions and the axially symmetric potential and Stokes flow function. The suggested method for the description of the above-mentioned fields is an analog of the method of analytic functions in the complex plane for the description of plane potential fields.
Similar content being viewed by others
References
E. T. Whittaker and G. N. Watson,A Course of Modern Analysis, Vol. 2, Cambridge University Press, Cambridge (1927).
L. G. Loitsyanskii,Mechanics of Liquid and Gas [in Russian], Nauka, Moscow 1987.
I. P. Mel’nichenko, “On a method for classification of potential flows with axial symmetry,” in:Contemporary Problems in Realand Complex Analysis [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984), pp. 98–102.
G. M. Fikhtengol’ts,A Course of Differential and Integral Calculus [in Russian], Vol. 2, Nauka, Moscow (1966).
M. A. Lavrent’ev and B. V. Shabat,Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1987).
P. P. Zabreiko et al.,Integral Equations [in Russian], Nauka, Moscow 1968.
Rights and permissions
About this article
Cite this article
Mel’nichenko, I.P., Plaksa, S.A. Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I. Ukr Math J 48, 1717–1730 (1996). https://doi.org/10.1007/BF02529493
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02529493