Semi-strong and strong solutions for variable density asymmetric fluids in unbounded domains

2016 ◽  
Vol 40 (3) ◽  
pp. 757-774 ◽  
Author(s):  
Pablo Braz e Silva ◽  
Felipe W. Cruz ◽  
Marko A. Rojas-Medar
Keyword(s):  
Unbounded Domains ◽  
Strong Solutions ◽  
Variable Density ◽  
Asymmetric Fluids

scholarly journals Local well-posedness of a quasi-incompressible two-phase flow

2020 ◽  
Author(s):  
Helmut Abels ◽  
Josef Weber
Keyword(s):  
Two Phase Flow ◽  
Type Equation ◽  
Strong Solutions ◽  
Variable Density ◽  
Diffuse Interface ◽  
Navier Stokes ◽  
Well Posedness ◽  
Phase Flow ◽  
Two Phase ◽  
Fluid Mixture

AbstractWe show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier–Stokes/Cahn–Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier–Stokes type equation. We prove existence of strong solutions locally in time with the aid of a suitable linearization and a contraction mapping argument. To this end, we show maximal $$L^2$$ L 2 -regularity for the Stokes part of the linearized system and use maximal $$L^p$$ L p -regularity for the linearized Cahn–Hilliard system.

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