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

Published online by Cambridge University Press:  02 December 2020

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.

Type
Research Article
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.

References

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