Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Helmut Abels
NWF I - Mathematik, Universität Regensburg, D-93040 Regensburg, GermanyMatthias Röger
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.
Cite this article
Helmut Abels, Matthias Röger, Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 6, pp. 2403–2424
DOI 10.1016/J.ANIHPC.2009.06.002