Recent Results for Diffuse Interface Systems Modeling Mixture of Two Incompressible Fluids
Host
Department of Applied Mathematics
Speaker
Andrea Giorgini
Department of Mathematics, Indiana University
https://math.indiana.edu/about/faculty/giorgini-andrea.html
Description
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 represented as the zero level set of a label function (or difference of fluid concentrations), whose values \(1\) and \(-1\) represent the pure phases. Free boundary problems are suitable limit of such Diffuse Interface systems. The kinematic condition of the interface translates into a transport equation for the label function. Two important regularizations, Allen-Cahn and Cahn-Hilliard dynamics, have 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 weak and regular solutions for viscous and inviscid fluids.
Event Topic
Stochastic & Multiscale Modeling and Computation