6 papers · 1 filter
On a visco-elastic Mullins-Sekerka System
Helmut Abels, Harald Garcke, Jonas Haselböck
We introduce a novel visco-elastic Mullins-Sekerka system with a prescribed constant contact angle at the boundary. The system is derived as an --type gradient flow of…
A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity
Harald Garcke, Jiashun Hu, Nuo Lei
We propose a gravity-consistent arbitrary Lagrangian--Eulerian finite element method for incompressible Navier--Stokes free-boundary problems with moving contact lines. A direct bo…
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…