scholarly journals Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

2012 ◽  
Vol 15 (3) ◽  
pp. 453-480 ◽  
Author(s):  
Helmut Abels ◽  
Daniel Depner ◽  
Harald Garcke
Keyword(s):  
Weak Solutions ◽  
Incompressible Fluids ◽  
Diffuse Interface ◽  
Interface Model ◽  
Two Phase Flows ◽  
Diffuse Interface Model ◽  
Two Phase ◽  
Existence Of Weak Solutions

scholarly journals On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids

2015 ◽  
Vol 35 (6) ◽  
pp. 2497-2522 ◽  
Author(s):  
Michela Eleuteri ◽  
◽  
Elisabetta Rocca ◽  
Giulio Schimperna ◽  
◽  
...  
Keyword(s):  
Incompressible Fluids ◽  
Diffuse Interface ◽  
Interface Model ◽  
Two Phase Flows ◽  
Diffuse Interface Model ◽  
Two Phase

scholarly journals Global existence of weak solutions for a nonlocal model for two-phase flows of incompressible fluids with unmatched densities

2016 ◽  
Vol 26 (10) ◽  
pp. 1955-1993 ◽  
Author(s):  
Sergio Frigeri
Keyword(s):  
Weak Solutions ◽  
Type System ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Diffuse Interface Model ◽  
Two Phase ◽  
Existence Of Weak Solutions ◽  
Cahn Hilliard Equation ◽  
The One ◽  
Three Space

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one recently derived by Abels, Garcke and Grün and consists in a Navier–Stokes type system coupled with a convective nonlocal Cahn–Hilliard equation. The density of the mixture depends on an order parameter. For this nonlocal system we prove existence of global dissipative weak solutions for the case of singular double-well potentials and non-degenerate mobilities. To this goal we devise an approach which is completely independent of the one employed by Abels, Depner and Garcke to establish existence of weak solutions for the local Abels et al. model.

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