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

Bogdan-Vasile Matioc; Georg Prokert

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arXiv · 2003.14010

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

Bogdan-Vasile Matioc·Georg Prokert

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Abstract

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.

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Bogdan-Vasile Matioc, Georg Prokert. 2020-03-31. Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials. https://arxiv.org/abs/2003.14010

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