Special Session 127: Nonlocal models arising in biology and ecology

Nonlocal-to-Local Convergence for a Diffuse Interface Model for Two Phase Flow with Matched Densities
Christoph Hurm
University of Regensburg
Germany
Co-Author(s):    Patrik Knopf, Andrea Poiatti
Abstract:
We prove convergence of a sequence of strong solutions to a diffuse interface model for the two-phase flow of incompressible fluids with matched densities with a nonlocal Cahn-Hilliard equation to the strong solution to the corresponding system with a standard local Cahn-Hilliard equation. The analysis is done in the case of constant viscosity. The proof is based on an energy method and convergence of the linearized operators in the Cahn-Hilliard equations.