SPRING 2021 Nonlinear Analysis Seminar Series
Associate Professor Yutaka Terasawa, Nagoya University
Title: Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities and Nonlocal Free Energies
We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions. In contrast to previous works, we study a model with a singular non-local free energy, which controls the fractional Sobolev norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization. This talk is based on joint work with Professor Helmut Abels (Regensburg).