We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed by Abels et al. for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier-Stokes system with a modified convective term coupled to a Cahn-Hilliard system. The density of the mixture depends on an order parameter. © 2012 Springer Basel.
CITATION STYLE
Abels, H., Depner, D., & Garcke, H. (2013). Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities. Journal of Mathematical Fluid Mechanics, 15(3), 453–480. https://doi.org/10.1007/s00021-012-0118-x
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