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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
71/2008

Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids

Helmut Abels and Matthias Röger

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.

Received:
Oct 21, 2008
Published:
Oct 27, 2008
MSC Codes:
35R35, 35Q30, 76D05, 76T99, 80A20
Keywords:
two-phase flow, navier-stokes, free boundary problems, mullins-sekerka

Related publications

inJournal
2009 Repository Open Access
Helmut Abels and Matthias Röger

Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids

In: Annales de l'Institut Henri Poincaré / C, 26 (2009) 6, pp. 2403-2424