Abels, Helmut and Roeger, Matthias (2009) Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 26 (6). pp. 2403-2424. ISSN 0294-1449,
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We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects into account. This leads to a coupled system of Navier-Stokes and Mullins-Sekerka type parts that coincides with the asymptotic limit of a diffuse interface model. We prove the long-time existence of weak solutions, which is an open problem for the classical two-phase model. We show that the phase interfaces have in almost all points a generalized mean curvature. (C) 2009 Elsevier Masson SAS. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GENERALIZED SOLUTIONS; PHASE-TRANSITIONS; ORDER-PARAMETER; MEAN-CURVATURE; EQUATION; Two-phase flow; Navier-Stokes; Free boundary problems; Mullins-Sekerka |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 02 Sep 2020 07:12 |
| Last Modified: | 02 Sep 2020 07:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/28164 |
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