ISOPERIMETRIC INEQUALITY FOR A CORNER HELE–SHAW DYNAMICS

DOI10.1142/S0219530505000595zbMath1078.30020OpenAlexW2069294533MaRDI QIDQ5313755

Alexander Vasil'ev

Publication date: 1 September 2005

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530505000595

zbMATH Keywords

free boundary problemisoperimetric inequalityharmonic potentialunivalent functionconformal mapHele-Shaw cellcomplex analysisHele-Shaw problemLaplacian equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) General theory of conformal mappings (30C35) Capacity and harmonic measure in the complex plane (30C85) Other free boundary flows; Hele-Shaw flows (76D27)

Cites Work

• Univalent functions in two-dimensional free boundary problems
• Moduli of families of curves for conformal and quasiconformal mappings
• Angular derivatives of bounded univalent functions and extremal partitions of the unit disk.
• Explicit solutions for Hele–Shaw corner flows
• Self-dilating viscous fingers in wedge-shaped Hele–Shaw cells
• Complex variable methods in Hele–Shaw moving boundary problems
• Flow around a wedge of arbitrary angle in a Hele-Shaw cell
• Hele-Shaw flows with free boundaries in a corner or around a wedge Part I: Liquid at the vertex
• Hele-Shaw flows with free boundaries in a corner or around a wedge Part II: Air at the vertex

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