A special class of univalent functions in Hele-Shaw flow problems (Q535999)
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scientific article; zbMATH DE number 5888162
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A special class of univalent functions in Hele-Shaw flow problems |
scientific article; zbMATH DE number 5888162 |
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A special class of univalent functions in Hele-Shaw flow problems (English)
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16 May 2011
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Summary: We study the time evolution of the free boundary of a viscous fluid for planar flows in Hele-Shaw cells under injection. Applying methods from the theory of univalent functions, we prove the invariance in time of \(\Phi \)-likeness property (a geometric property which includes starlikeness and spiral-likeness) for two basic cases: the inner problem and the outer problem. We study both zero and nonzero surface tension models. Certain particular cases are also presented.
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