Matioc, Bogdan-Vasile (2019) THE MUSKAT PROBLEM IN TWO DIMENSIONS: EQUIVALENCE OF FORMULATIONS, WELL-POSEDNESS, AND REGULARITY RESULTS. ANALYSIS & PDE, 12 (2). pp. 281-332. ISSN 1948-206X,
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We consider the Muskat problem describing the motion of two unbounded immiscible fluid layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first prove that the mathematical model can be formulated as an evolution problem for the sharp interface separating the two fluids, which turns out to be, in a suitable functional-analytic setting, quasilinear and of parabolic type. Based upon these properties, we then establish the local well-posedness of the problem for arbitrary large initial data and show that the solutions become instantly real-analytic in time and space. Our method allows us to choose the initial data in the class H-s, s is an element of (3/2, 2), when neglecting surface tension, respectively in H-s, s is an element of (2, 3), when surface-tension effects are included. Besides, we provide new criteria for the global existence of solutions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SURFACE-TENSION; HELE-SHAW; GLOBAL EXISTENCE; TURNING WAVES; FREE-BOUNDARY; POROUS-MEDIUM; INTERFACE; WATER; PARABOLICITY; STABILITY; Muskat problem; surface tension; singular integral |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 22 Apr 2020 10:28 |
| Last Modified: | 22 Apr 2020 10:28 |
| URI: | https://pred.uni-regensburg.de/id/eprint/27959 |
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