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Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids. (English) Zbl 1181.35343

Summary: 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.

MSC:

35R35 Free boundary problems for PDEs
35Q30 Navier-Stokes equations
76D45 Capillarity (surface tension) for incompressible viscous fluids
76T99 Multiphase and multicomponent flows
80A20 Heat and mass transfer, heat flow (MSC2010)
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References:

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