scholarly journals Global existence of weak solutions to a diffuse interface model for magnetic fluids

2021 ◽  
Vol 59 ◽  
pp. 103243
Author(s):  
Martin Kalousek ◽  
Sourav Mitra ◽  
Anja Schlömerkemper
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
Magnetic Fluids ◽  
Diffuse Interface ◽  
Interface Model ◽  
Diffuse Interface Model ◽  
Existence Of Weak Solutions

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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