The multiphase Muskat problem with equal viscosities in two dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929326650294272 |
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| author | Bierler, Jonas Matioc, Bogdan-Vasile |
| author_facet | Bierler, Jonas Matioc, Bogdan-Vasile |
| contents | We study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with equal viscosities in a vertical homogeneous porous medium identified with $\mathbb{R}^2$ under the effect of gravity. We first formulate the governing equations as a strongly coupled evolution problem for the functions that parameterize the sharp interfaces between the fluids. Afterwards we prove that the problem is of parabolic type and establish its well-posedness together with two parabolic smoothing properties. For solutions that are not global we exclude, in a certain regime, that the interfaces come into contact along a curve segment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_07728 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The multiphase Muskat problem with equal viscosities in two dimensions Bierler, Jonas Matioc, Bogdan-Vasile Analysis of PDEs 35R37, 76D27, 35K55 We study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with equal viscosities in a vertical homogeneous porous medium identified with $\mathbb{R}^2$ under the effect of gravity. We first formulate the governing equations as a strongly coupled evolution problem for the functions that parameterize the sharp interfaces between the fluids. Afterwards we prove that the problem is of parabolic type and establish its well-posedness together with two parabolic smoothing properties. For solutions that are not global we exclude, in a certain regime, that the interfaces come into contact along a curve segment. |
| title | The multiphase Muskat problem with equal viscosities in two dimensions |
| topic | Analysis of PDEs 35R37, 76D27, 35K55 |
| url | https://arxiv.org/abs/2101.07728 |