Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Univalent Functions in the Dynamics of Viscous Flows

Univalent Functions in the Dynamics of Viscous Flows The main goal of the paper is to apply methods of the theory of univalent functions to some problems of fluid mechanics. Our interest centers on free boundary problems. We study the time evolution of the free boundary of a viscous fluid in the zero- and non-zero-surface-tension models for planar flows in Hele-Shaw cells either with an extending to infinity free boundary or with a bounded free boundary. We consider special classes of univalent functions which admit an explicit geometric interpretation to characterize the shape of the free interface. The paper contains a survey part as well as new results. We also set up some new problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Univalent Functions in the Dynamics of Viscous Flows

Loading next page...
 
/lp/springer-journals/univalent-functions-in-the-dynamics-of-viscous-flows-hTeMuStuUC
Publisher
Springer Journals
Copyright
Copyright © 2001 by Heldermann Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03320993
Publisher site
See Article on Publisher Site

Abstract

The main goal of the paper is to apply methods of the theory of univalent functions to some problems of fluid mechanics. Our interest centers on free boundary problems. We study the time evolution of the free boundary of a viscous fluid in the zero- and non-zero-surface-tension models for planar flows in Hele-Shaw cells either with an extending to infinity free boundary or with a bounded free boundary. We consider special classes of univalent functions which admit an explicit geometric interpretation to characterize the shape of the free interface. The paper contains a survey part as well as new results. We also set up some new problems.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Mar 7, 2013

References