On an extremal problem of airfoil theory
type: Item
instance of: scholarly article
title: On an extremal problem of airfoil theory
zbMATH Open document ID: 0984.30014
author: R. Smith
published in: Russian Mathematics
publication date: 2001-06-27T00:00:00Z
review text: A certain problem in fluid dynamics involves finding extremal functions for a situation involving an ideal incompressible fluid, a given angle of attack and a velocity that is constant at infinity [\textit{F. G. Avkhadiev}, \textit{A. M. Elizarov} and \textit{D. A. Fokin}, Eur. J. Appl. Math. 6, No. 5, 385-398 (1995; Zbl 0840.76025)]. The extremal functions are to provide the minimum of the maximal velocities of the flow. This problem was reduced to a problem in the class \(\Sigma\) of functions \(F(z)=z+a_0 +\sum^\infty_{n=1} a_n z^{-n}\) univalent in \(|z|>1\). The author proves that with certain assumptions, the extremal functions are slit mappings. The author uses tools both from geometric function theory and fluid dynamics.
reviewed by: Renate McLaughlin
Mathematics Subject Classification ID: 30C70
Mathematics Subject Classification ID: 30C75
Mathematics Subject Classification ID: 76B10
zbMATH DE Number: 1542160
zbMATH Keywords: simply-connected domain
zbMATH Keywords: class \(\Sigma\) of univalent functions
zbMATH Keywords: slit mapping
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1542160