Year: 2025
Type: article
Abstract: In this paper, we study the two-dimensional multiphase Muskat problem describing the motion of three immiscible fluids with general viscosities in a vertical homogeneous porous medium under the influence of gravity. Employing Rellich-type identities in the regime where the fluids are ordered according to their viscosities, and a Neumann series argument when the fluids are not ordered by viscosity, we may recast the governing equations as a strongly coupled nonlinear and nonlocal evolution problem for the functions that parameterize the sharp interfaces that separate the fluids. This problem is of parabolic type if the Rayleigh-Taylor condition is satisfied at each interface. Based on this property, we then show that the multiphase Muskat problem is well-posed in all $ L_2 $-subcritical Sobolev spaces and that it features some parabolic smoothing properties.
DOI: 10.3934/dcds.2025089
Authors: Jonas Bierler, Bogdan-Vasile Matioc
Institution: University of Regensburg
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Deutsche Forschungsgemeinschaft
Award: G3270504644
OpenAlex ID: W4411383914