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Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids
Helmut Abels and Matthias RögerAbstract
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:
- 21.10.08
- Published:
- 27.10.08
- MSC Codes:
- 35R35, 35Q30, 76D05, 76T99, 80A20
- Keywords:
- two-phase flow, navier-stokes, free boundary problems, mullins-sekerka