Speaker
Description
Viscoelastic phase separation occurs in binary fluids where the constituent molecules aggregate on strongly different time scales. Typically, the morphology of this process features volume shrinking, sponge-like structures and phase inversion. Such phenomena are observed in polymer solutions, for instance, where polymer chains are much larger and migrate much more slowly compared to solvent molecules.
In this talk, we consider a dissipative diffuse-interface model, introduced by Zhou, Zhang and E (2006), which couples a Cahn–Hilliard equation for the phase variable with the spherical part of the bulk stress, governed by relaxation dynamics. Our main objective is to establish existence of weak solutions and (conditional) weak–strong uniqueness, assuming degenerate mobility functions and possibly singular potentials. The analysis follows a gradient flow approach with an underlying metric of Benamou–Brenier (Wasserstein) type that reflects a coupled system of two equations. Two aspects prove particularly challenging: the absence of a classical Euler–Lagrange equation and the task of establishing convexity of the internal energy functional.