Bierler, Jonas and Matioc, Bogdan-Vasile (2022) The multiphase Muskat problem with equal viscosities in two dimensions. INTERFACES AND FREE BOUNDARIES, 24 (2). pp. 163-196. ISSN 1463-9963, 1463-9971
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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 R2 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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | WELL-POSEDNESS; SPLASH SINGULARITIES; POROUS-MEDIA; 3-PHASE FLOW; HELE-SHAW; INTERFACE; REGULARITY; EXISTENCE; FLUIDS; Multiphase Muskat problem; parabolic evolution equation; singular integral; subcritical spaces |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 07:12 |
| Last Modified: | 07 Feb 2024 07:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56593 |
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