Helmut Abels - Diffuse and Sharp Interface Models for Two Phase Flows

Explore a comprehensive lecture on diffuse and sharp interface models for two-phase flows of incompressible, viscous Newtonian fluids. Delve into an overview of analytic results and recent findings on the asymptotic limits of diffuse interface models as the interfacial thickness approaches zero. Examine the basic modeling assumptions, diffuse interface models (Model H), and the structure of proofs involving separate systems. Investigate the sharp interface limit of the Cahn-Hilliard equation and matched asymptotics. Learn about the existence of local strong and global weak solutions for cases with equal densities. Gain insights into rigorous analytic results for sharp interface limits, including the Stokes Cahn-Hilliard system and refined spectral estimates.

Intro
Basic Modeling Assumptions
Diffuse Interface Model - Model H We consider
Diffuse Interface Model - Madel H We consider
Structure of the Proof First study the separate systems
Sharp Interface Limit of Cahn-Hilliard Equation We consider
Sharp Interface Limits via Matched Asymptotics (AGG '12)
Overview of Analytic Results (Case of Same Densities) Existence of local strong global weak solutions
Sharp Interface Limit: Rigorous Analytic Results
Sharp Interface Limit for a Stokes Cahn-Hilliard System
Refined Spectral Estimate