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

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

2008-10-22

arxiv.org/abs/0810.3987v1

Mathematics

Analysis of PDEs

26 pages

Scientific paper

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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