Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous,incompressible fluids |
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Authors: | Helmut Abels Matthias Röger |
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Institution: | 1. NWF I - Mathematik, Universität Regensburg, D-93040 Regensburg, Germany;2. Hausdorff Center for Mathematics, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany |
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Abstract: | 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. |
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Keywords: | primary 35R35 secondary 35Q30 76D45 76T99 80A20 |
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