TY  - JOUR
A1  - Bierler, Jonas
A1  - Matioc, Bogdan-Vasile
PB  - EUROPEAN MATHEMATICAL SOC-EMS
SN  - 1463-9963
SN  -  1463-9971
EP  - 196
ID  - epub56955
KW  - 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
JF  - Interfaces and Free Boundaries
AV  - none
SP  - 163
TI  - The multiphase Muskat problem with equal viscosities in two dimensions
VL  - 24
N2  - 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.
IS  - 2
UR  - http://doi.org/10.4171/IFB/469
CY  - BERLIN
Y1  - 2021///
ER  -