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Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials

Part of: Miscellaneous topics - Partial differential equations Parabolic equations and systems Incompressible viscous fluids

Published online by Cambridge University Press:  02 December 2020

Bogdan–Vasile Matioc Open the ORCID record for Bogdan–Vasile Matioc [Opens in a new window]  and
Georg Prokert
Bogdan–Vasile Matioc
Affiliation:
Fakultät für Mathematik, Universität Regensburg, 93040 Regensburg, Deutschland (bogdan.matioc@ur.de)
Georg Prokert
Affiliation:
Faculty of Mathematics and Computer Science, Technical University Eindhoven, The Netherlands (g.prokert@tue.nl)
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Abstract

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We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.

Keywords

Stokes problemtwo-phasesingular integralscontour integral formulation

MSC classification

Primary: 35R37: Moving boundary problems
Secondary: 76D07: Stokes and related (Oseen, etc.) flows 35K55: Nonlinear parabolic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1815 - 1845
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press.

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