Matioc, Anca-Voichita and Matioc, Bogdan-Vasile (2023) A new reformulation of the Muskat problem with surface tension. JOURNAL OF DIFFERENTIAL EQUATIONS, 350. pp. 308-335. ISSN 0022-0396, 1090-2732
Full text not available from this repository. (Request a copy)Abstract
Two formulas that connect the derivatives of the double layer potential and of a related singular integral operator evaluated at some density 6 to the L2-adjoints of these operators evaluated at the density 6' are used to recast the Muskat problem with surface tension and general viscosities as a system of equations with nonlinearities expressed in terms of the L2-adjoints of these operators. An advantage of this formulation is that the nonlinearities appear now as a derivative. This aspect and abstract quasilinear parabolic theory are then exploited to establish a local well-posedness result in all subcritical Sobolev spaces Wps (R) with p E (1,co) and s E (1 + 1/p, 2). (c) 2023 Elsevier Inc. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | WELL-POSEDNESS; POROUS-MEDIA; PARABOLICITY; REGULARITY; STABILITY; LIMIT; LAYER; Muskat problem; Surface tension; Singular integral operator; Well-posedness |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 30 Jan 2024 15:20 |
| Last Modified: | 30 Jan 2024 15:20 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59019 |
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