Published 2025-08-11
DOI:
https://doi.org/10.71712/Keywords
- free boundary problem,
- conformal map,
- complex analysis,
- univalent function,
- hypergeometric function
Copyright (c) 2025 Scientia Series A: Mathematical Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
Markina, I., & Vasiliev, A. (2025). Long-pin perturbations of the trivial solution for Hele-Shawcorner flows. Scientia Series A: Mathematical Sciences, 9, 33-43. https://doi.org/10.71712/
Abstract
We consider two-dimensional Hele-Shaw corner flows without effect of the surface tension and with an interface extending to the infinity along one of the walls. Explicit solutions that present a ”long-pin” deformations of the trivial solution are got. Making use of the Polubarinova-Galin approach we derive parametric equations for the moving interface in terms of univalent mappings of a canonical domain. For the right angle we repeat a result by Leo P. Kadanoff.
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