Talk by Maurizio Grasselli
A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard equation. This system describes the evolution of an incompressible isothermal mixture of fluids and it has been investigated by many authors. Here I want to discuss a variant of this model where the standard Cahn-Hilliard equation is replaced by its nonlocal version. More precisely, the gradient term in the free energy functional is replaced by a spatial convolution operator acting on the order parameter. I intend to present some recent results on the global longtime behavior of the (weak) solutions.