# On a free boundary problem for polymeric fluids: Global existence of weak solutions

## TL;DR

This paper proves the global existence of weak solutions for a free boundary problem modeling polymeric fluids, using asymptotic analysis of a macroscopic suspension model as the adiabatic exponent tends to infinity.

## Contribution

It introduces a novel approach to establish weak solutions for a free boundary problem in polymeric fluids via asymptotic limits of the Doi-Model.

## Key findings

- Weak solutions constructed for the two-phase model.
- Convergence of solutions to the free-boundary problem proven.
- Techniques extend Lions and Masmoudi's methods to this context.

## Abstract

We investigate the stability and global existence of weak solutions to a free boundary problem governing the evolution of polymeric fluids. We construct weak solutions of the two-phase model by performing the asymptotic limit of a macroscopic model governing the suspensions of rod-like molecules (known as Doi-Model) in compressible fluids as the adiabatic exponent $\gamma$ goes to $\infty.$ 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 \cite{LionsMasmoudi-1999}.