Boehme, Daniel and Matioc, Bogdan-Vasile (2025) Well-posedness and stability for the two-phase periodic quasistationary Stokes flow. INTERFACES AND FREE BOUNDARIES, 27 (4). pp. 659-701. ISSN 1463-9963, 1463-9971
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The two-phase horizontally periodic quasistationary Stokes flow in R2, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, parameterized as the graph of a function f = f (t), is considered in the general case when both gravity and surface tension effects are included. Using potential theory, the moving boundary problem is formulated as a fully nonlinear and nonlocal parabolic problem for the function f. Based on abstract parabolic theory, it is shown that the problem is well-posed in all subcritical spaces Hr (S), with r E (3/2, 2). Moreover, the stability properties of the flat equilibria are analyzed in dependence on the physical properties of the fluids.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PESKIN PROBLEM; CAPILLARY DROP; STATIC MOTION; SEDIMENTATION; PARTICLES; periodic Stokes flow; well-posedness; stability; gravity; surface tension |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 02 Jun 2026 09:19 |
| Last Modified: | 02 Jun 2026 09:19 |
| URI: | https://pred.uni-regensburg.de/id/eprint/65913 |
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