Solutions of a free boundary problem in a doubly connected domain via a circular-arc polygon

Author:

MARSHALL J. S.

Abstract

This paper addresses a free boundary problem for a steady, uniform patch of vorticity surrounding a single flat plate of zero thickness and finite length. Exact solutions to this problem have previously been found in terms of conformal maps represented by Cauchy-type integrals. Here, however, it is demonstrated how, by considering an associated circular-arc polygon and using ideas from automorphic function theory, these maps can be expressed in a simple non-integral form.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Exact solutions for Hele-Shaw free boundary flows around a flat plate of finite length;The Quarterly Journal of Mechanics and Applied Mathematics;2015-11-24

2. Analytical solutions for Hele-Shaw moving boundary flows in the presence of a circular cylinder;The Quarterly Journal of Mechanics and Applied Mathematics;2015-11-24

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