2011 | OriginalPaper | Chapter
Double Obstacle Limit for a Navier-Stokes/Cahn-Hilliard System
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We consider the double obstacle limit for a Navier-Stokes/Cahn- Hilliard type system. The system describes a so-called diffuse interface model for the two-phase flow of two macroscopically immiscible incompressible viscous fluids in the case of matched densities, also known as Model H. Starting with a suitable class of singular free energies, which keep the concentration strictly inside the physically reasonable interval [
a, b
], we analyze a certain singular limit, where the equation for the chemical potential converges to a differential inclusion related to the subgradient of the indicator function of [
a, b
].