Strong well-posedness of a diffuse interface model for a viscous, quasi-incompressible two-phase flow.
Preprintreihe der Fakultät Mathematik 20/2011,
We study a diffuse interface model for the flow of two viscous incompressible Newtonian fluids 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. In contrast to previous works, we study a model for the general case that the
fluids have different densities due to Lowengrub and Truskinovski . This leads to an inhomogeneous Navier-Stokes system coupled to a Cahn-Hilliard system, where the density of the mixture depends on the concentration, the velocity field is no longer divergence free, and the pressure
enters the equation for the chemical potential. We prove existence of unique strong solutions for the non-stationary system for sufficiently small times.
|Item Type:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Helmut Abels|
|Keywords:||Two-phase flow, free boundary value problems, diffuse interface model, mixtures of viscous fluids, Cahn-Hilliard equation, inhomogeneous Navier-Stokes equation|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||18 Apr 2011 06:23|
|Last Modified:||06 Sep 2011 07:00|