Singularity of Integral Equations with the Cauchy Kernel on a Closed Contour in Hydrodynamic Problems
D. N. Gorelov
Sobolev Institute of the Mathematics, Siberian Branch, Russian Academy of Sciences, Omsk, Russia, 644043
Keywords: сингулярные интегральные уравнения, интеграл Коши, формулы Сохоцкого-Племели, singular integral equations, Cauchy integral, Sochocki-Plemelj formulas
Abstract
Singular integral equations of the first and second kind with the Cauchy kernel on a limiting narrow closed contour are theoretically considered. The initial equations are found to degenerate on the limiting contour. This singularity of integral equations with the Cauchy kernel does not allow boundary-value problems of the flow around thin airfoils to be solved correctly; therefore, a system consisting of integral equations of the first and second kind is proposed for solving such problems. The results of the present study are tested against an exact solution of the problem of the flow past a flat plate.
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