Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2003_14010 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials Matioc, Bogdan-Vasile Prokert, Georg Analysis of PDEs 35R37, 76D07, 35K55 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. |
| title | Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials |
| topic | Analysis of PDEs 35R37, 76D07, 35K55 |
| url | https://arxiv.org/abs/2003.14010 |