Some geometrical properties of free boundaries in the Hele-Shaw flows

Paula Curt and Mirela Kohr

Applied Mathematics and Computation, 2018, vol. 323, issue C, 86-94

Abstract: In this paper, we are concerned with certain geometric properties of the moving boundary in the case of two-dimensional viscous fluid flows in Hele-Shaw cells under injection. We study the invariance in time of free boundary for such a bounded flow domain under the assumption of zero surface tension. By applying various results in the theory of univalent functions, we consider the invariance in time of starlikeness of a complex order, almost starlikeness of order α ∈ [0, 1), and almost spirallikeness of type γ∈(−π/2,π/2) and order α ∈ (0, cos γ). This work complements recent work on planar Hele-Shaw flow problems in the case of zero surface tension.

Keywords: Blow up time; Free boundary; Hele-Shaw flow; Spirallikeness; Starlikeness; Univalent function (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:323:y:2018:i:c:p:86-94

DOI: 10.1016/j.amc.2017.11.051

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