The seminar is sponsored by NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai.
Abstract:
We will discuss so-called "diffuse interface models" for the flow of two viscous incompressible Newtonian fluids in a bounded domain. Such models were introduced to describe the flow when singularities in the interface, which separates the fluids, (droplet formation/coalescence) occur. The fluids are assumed to be macroscopically immiscible, but a partial mixing in a small interfacial region is assumed in the model. Such kind of models became popular during the last decade for theoretical as well as numerical studies. We will give an overview of known analytic results on well-posedness and will discuss briefly their relation to classical and non-classical sharp interface models.
Biography:
Helmut Abels is a Professor of Mathematics at University Regensburg, Germany. His research interests include: partial differential equations and mathematical fluid mechanics, in particular Navier-Stokes equations and other models for viscous fluids; free boundary value problems, phase separation and phase transition, diffuse interface models for free boundary value problems; pseudodifferential boundary value problems and pseudodifferential operators with non-smooth coefficients; and regularity of solutions of elliptic and parabolic systems.