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

100%

Abels H.

Banach Center Publications

2009

tom 86

nr 1

9-19

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 existence, uniqueness and regularity of weak and strong solutions in two and three space dimensions. Moreover, we prove stability of local minima of the energy and show existence of a weak global attractor, which is strong if d = 2.

Stokes equations in asymptotically flat layers

100%

Abels H.

Banach Center Publications

2005

tom 70

nr 1

9-19

We study the generalized Stokes resolvent equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer $Ω₀ = ℝ^{n-1} × (-1,1)$. 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 of its consequences, which also yields an application to a free boundary value problem.

Ograniczanie wyników

2 Banach Center Publications

2 Abels H.

1 2009

1 2005

Wyniki wyszukiwania

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

Stokes equations in asymptotically flat layers