Matioc, Bogdan-Vasile and Prokert, Georg (2023) Capillarity-driven Stokes flow: the one-phase problem as small viscosity limit. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 74 (6): 212. ISSN 0044-2275, 1420-9039
Full text not available from this repository. (Request a copy)Abstract
We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of singular integrals. We prove well-posedness of the problem in the subcritical Sobolev spaces H-s(R) up to critical regularity, and establish parabolic smoothing properties for the solutions. Moreover, we identify the problem as the singular limit of the two-phase quasistationary Stokes flow when the viscosity of one of the fluids vanishes.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUASI-STATIC MOTION; MUSKAT PROBLEM; INTERFACE; SEDIMENTATION; REGULARITY; PARTICLES; DROP; Quasistationary Stokes problem; Singular integrals; Single layer potential |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 05 Mar 2024 12:20 |
| Last Modified: | 05 Mar 2024 12:20 |
| URI: | https://pred.uni-regensburg.de/id/eprint/59321 |
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