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arXiv · 2406.07181

Well-posedness and stability for the two-phase periodic quasistationary Stokes flow

Daniel Böhme·Bogdan-Vasile Matioc
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Abstract

The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a function $f=f(t)$, is considered in the general case when both gravity and surface tension effects are included. Using potential theory, the moving boundary problem is formulated as a fully nonlinear and nonlocal parabolic problem for the function $f$. Based on abstract parabolic theory, it is proven that the problem is well-posed in all subcritical spaces $\mathrm{H}^r(\mathbb{S})$, $r\in(3/2,2)$. Moreover, the stability properties of the flat equilibria are analyzed in dependence on the physical properties of the fluids.

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Daniel Böhme, Bogdan-Vasile Matioc. 2024-06-11. Well-posedness and stability for the two-phase periodic quasistationary Stokes flow. https://arxiv.org/abs/2406.07181

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