Bierler, Jonas and Matioc, Bogdan-Vasile (2025) THE MULTIPHASE MUSKAT PROBLEM WITH GENERAL VISCOSITIES IN TWO DIMENSIONS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 45 (12). pp. 5222-5250. ISSN 1078-0947, 1553-5231
Full text not available from this repository.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 L2-subcritical Sobolev spaces and that it features some parabolic smoothing properties.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | WELL-POSEDNESS; HELE-SHAW; SPLASH SINGULARITIES; POROUS-MEDIUM; 3-PHASE FLOW; REGULARITY; INTERFACE; FLUIDS; MEDIA; Muskat problem; parabolic evolution equation; singular integral; well posedness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2026 09:01 |
| Last Modified: | 06 May 2026 09:01 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65903 |
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