On an extremal problem of airfoil theory
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.
scientific article; zbMATH DE number 1542160