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

• Autorzy: Helmut Abels
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 76D27: Other free-boundary flows; Hele-Shaw flows
• 76D03: Existence, uniqueness, and regularity theory
• 76D45: Capillarity (surface tension)
• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations
• 35Q35: PDEs in connection with fluid mechanics
• 76T99: None of the above, but in this section
• 35B40: Asymptotic behavior of solutions
• 35B41: Attractors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 86
• Numer: 1
• Strony: 9-19

Daty

wydano

2009

Twórcy

autor

Helmut Abels

• Max Planck Institute for Mathematics in Science, Inselstr. 22, 04103 Leipzig, Germany

Identyfikatory

DOI

10.4064/bc86-0-1