Geodesic
The multiphase Muskat problem with equal viscosities in two dimensions
Jonas Bierler1 ; Bogdan-Vasile Matioc1 orcid
1Universität Regensburg, Germany
Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 163-196

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DOI

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.
DOI : 10.4171/ifb/469
Classification : 35-XX, 76-XX
Mots-clés : Multiphase Muskat problem, parabolic evolution equation, singular integral, subcritical spaces

Jonas Bierler  1   ; Bogdan-Vasile Matioc  1

1 Universität Regensburg, Germany 
Jonas Bierler; Bogdan-Vasile Matioc. The multiphase Muskat problem with equal viscosities in two dimensions. Interfaces and free boundaries, Tome 24 (2022) no. 2, pp. 163-196. doi: 10.4171/ifb/469
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     title = {The multiphase {Muskat} problem with equal viscosities in two dimensions},
     journal = {Interfaces and free boundaries},
     pages = {163--196},
     year = {2022},
     volume = {24},
     number = {2},
     doi = {10.4171/ifb/469},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/469/}
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