Global existence of weak solutions to viscoelastic phase separation part: I. Regular case

Abstract

Abstract We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn–Hilliard-type equation for two-phase flows and the Peterlin–Navier–Stokes equations for viscoelastic fluids. We focus on the case of a polynomial-like potential and suitably bounded coefficient functions. Using the Lagrange–Galerkin finite element method complex behavior of solution for spinodal decomposition including transient polymeric network structures is demonstrated.