APDEs Seminar

Diffuse Interface models are nowadays widely employed in Fluid Dynamics to model the free interface motion of mixtures of two different fluids (or phases). In this approach, the interface is the zero level set of the order parameter, which represents the difference of the fluid concentrations. Free boundary problems are suitable limit of Diffuse Interface systems. The kinematic condition of the interface translates into a transport equation for the order parameter. A well-known regularization is the conserved Allen-Cahn dynamics, which has been introduced in literature to account for a partial mixing of fluids occurring at the interface. In this talk I will present some recent results concerning the existence and uniqueness of solutions for nonhomogeneous viscous incompressible binary mixtures. This is a joint work with Maurizio Grasselli (Politecnico di Milano) and Hao Wu (Fudan University).