8 papers · 1 filter
Local Well-Posedness for a Diffuse Interface Model for Two-Phase Flows from Mixture Theory
Helmut Abels, Harald Garcke, Julia Wittmann
Local-in-time well-posedness is established for a recently proposed diffuse interface model describing incompressible two-phase flows. The result constitutes the first analytical s…
Weak and strong solutions for a class of quasilinear Allen--Cahn systems
Harald Garcke, Tim Laux, Andrea Poiatti
We consider a quasilinear Allen--Cahn system which arises when the gradient energy term in the Ginzburg--Landau energy also contains zero order terms. Such systems offer significan…
Analysis of a Cahn-Hilliard-Canham-Helfrich system for the evolution of a two-phase membrane
Harald Garcke, Mathias Wilke
The coupling of the evolution of a surface with evolution equations defined on that surface is of relevance in many applications and has been in the focus of interest in the analys…
On a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities: Energy equality and Lyapunov stability
Harald Garcke, Maoyin Lv, Hao Wu
We consider the initial-boundary value problem of a thermodynamically consistent diffuse interface model for incompressible two-phase flows with unmatched densities in a bounded do…
Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
Helmut Abels, Harald Garcke, Andrea Poiatti
A Cahn-Hilliard-Navier-Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn-Hilliard…
Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
Helmut Abels, Harald Garcke, Julia Wittmann
The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transitio…