Matioc, Bogdan-Vasile and Prokert, Georg (2021) Two-phase Stokes flow by capillarity in full 2D space: an approach via hydrodynamic potentials. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 151 (6). pp. 1815-1845. ISSN 0308-2105, 1473-7124
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We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MUSKAT PROBLEM; INTERFACE; REGULARITY; Stokes problem; two-phase; singular integrals; contour integral formulation |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 28 Jul 2022 08:43 |
| Last Modified: | 28 Jul 2022 08:43 |
| URI: | https://pred.uni-regensburg.de/id/eprint/46124 |
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