Well-posedness and stability for the two-phase periodic quasistationary Stokes flow
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916283072643072 |
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| author | Böhme, Daniel Matioc, Bogdan-Vasile |
| author_facet | Böhme, Daniel Matioc, Bogdan-Vasile |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness and stability for the two-phase periodic quasistationary Stokes flow Böhme, Daniel Matioc, Bogdan-Vasile Analysis of PDEs 31A10, 35B35, 35B65, 35K55, 76D07 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. |
| title | Well-posedness and stability for the two-phase periodic quasistationary Stokes flow |
| topic | Analysis of PDEs 31A10, 35B35, 35B65, 35K55, 76D07 |
| url | https://arxiv.org/abs/2406.07181 |