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Longtime behavior of solutions of a Navier-Stokes/Cahn-Hilliard system

Helmut Abels — 2009

Banach Center Publications

We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids of the same density in a bounded domain. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Moreover, diffusion of both components is taken into account. This leads to a coupled Navier-Stokes/Cahn-Hilliard system, which can describe the evolution of droplet formation and collision during the flow. We review some results on...

Stokes equations in asymptotically flat layers

Helmut Abels — 2005

Banach Center Publications

We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer Ω ₀ = ℝ n - 1 × ( - 1 , 1 ) . Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. We discuss the results on unique solvability of the generalized Stokes resolvent equations as well as the existence of a bounded H ∞ -calculus for the associated Stokes operator and some...

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