Nonlocal Cahn-Hilliard-Hele-Shaw Systems

Explore the intricacies of Nonlocal Cahn-Hilliard-Hele-Shaw systems in this 48-minute lecture by Maurizio Grasselli from Politecnico di Milano. Delve into the approximation of the Navier-Stokes-Cahn-Hilliard system for incompressible binary flow in a two-dimensional Hele-Shaw cell, and its applications in three-dimensional fluid flow in porous media and solid tumor growth modeling. Examine recent findings on a nonlocal CHHS system with degenerate mobility, singular potential, and nonconstant kinematic viscosity. Investigate well-posedness and regularity issues, and compare results with similar systems. This lecture, part of a joint project with C. Cavaterra and S. Frigeri from Universita degli Studi di Milano, offers valuable insights into advanced fluid dynamics and mathematical modeling.