Two-phase Stokes flow by capillarity in the plane: The case of different viscosities
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arXiv
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| Format: | Preprint |
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2021
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| author | Matioc, Bogdan-Vasile Prokert, Georg |
| author_facet | Matioc, Bogdan-Vasile Prokert, Georg |
| contents | We study the two-phase Stokes flow driven by surface tension for two fluids of different viscosities, separated by an asymptotically flat interface representable as graph of a differentiable function. 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 and double layer potential, spectral results on the corresponding integral operators, and abstract results on nonlinear parabolic evolution equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_12814 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Two-phase Stokes flow by capillarity in the plane: The case of different viscosities Matioc, Bogdan-Vasile Prokert, Georg Analysis of PDEs 35R37, 76D07, 35K55 We study the two-phase Stokes flow driven by surface tension for two fluids of different viscosities, separated by an asymptotically flat interface representable as graph of a differentiable function. 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 and double layer potential, spectral results on the corresponding integral operators, and abstract results on nonlinear parabolic evolution equations. |
| title | Two-phase Stokes flow by capillarity in the plane: The case of different viscosities |
| topic | Analysis of PDEs 35R37, 76D07, 35K55 |
| url | https://arxiv.org/abs/2102.12814 |