Applied Math Colloquium: Dr. Konstantina Trivisa

Title: Analysis on models for polymeric fluids: On the suspension of rod-like and bead-like molecules

Abstract:

In this talk I will present results on the stability and global existence of weak solutions to models describing the evolutions of polymeric fluids. The analysis covers the Doi model for the suspension of rod-like molecules within both an incompressible  and a compressible fluid within a bounded domain, as well as the free boundary problem governing the evolution of finitely extensible bead-spring chains in dilute polymers. We construct weak solutions of the two-phase model by performing the asymptotic limit as the adiabatic exponent γ goes to infinity for a macroscopic model which arises from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymeric molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. This class of models involves the unsteady, compressible, isentropic, isothermal Navier-Stokes system in a bounded domain Ω in two and three space dimensions. The convergence of these solutions, up to a subsequence, to the free-boundary problem is established using techniques in the spirit of Lions and Masmoudi (1999).