Abels, Helmut and Matioc, Bogdan-Vasile (2022) Well-posedness of the Muskat problem in subcritical L-p-Sobolev spaces. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 33 (2). pp. 224-266. ISSN 0956-7925, 1469-4425
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We study the Muskat problem describing the vertical motion of two immiscible fluids in a two-dimensional homogeneous porous medium in an L-p-setting with p is an element of (1, infinity). The Sobolev space W-p(s)(R) with s = 1 + 1/p is a critical space for this problem. We prove, for each s is an element of (1+1/p, 2) that the Rayleigh-Taylor condition identifies an open subset of W-p(s)(R) within which the Muskat problem is of parabolic type. This enables us to establish the local well-posedness of the problem in all these subcritical spaces together with a parabolic smoothing property.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SINGULAR INTEGRAL-OPERATORS; GLOBAL EXISTENCE; HELE-SHAW; TURNING WAVES; POROUS-MEDIA; INTERFACE; WATER; PARABOLICITY; BOUNDEDNESS; REGULARITY; Muskat problem; Rayleigh-Taylor condition; subcritical space; singular integral |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Petra Gürster |
| Date Deposited: | 22 May 2024 09:54 |
| Last Modified: | 22 May 2024 09:54 |
| URI: | https://pred.uni-regensburg.de/id/eprint/45760 |
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