# The incompressible limit of compressible finitely extensible nonlinear bead-spring chain models for dilute polymeric fluids

## TL;DR

This paper investigates the transition of dilute polymeric fluid models from compressible to incompressible regimes, demonstrating the limiting behavior of solutions as the Mach number approaches zero.

## Contribution

It establishes the rigorous incompressible limit for a class of bead-spring chain models with nonlinear elastic springs in dilute polymeric fluids.

## Key findings

- Weak solutions converge to incompressible models as Mach number tends to zero.
- The study confirms the validity of incompressible approximation in dilute polymeric fluids.
- Results are obtained for models with FENE spring potentials and slip boundary conditions.

## Abstract

We explore the behaviour of global-in-time weak solutions to a class of bead-spring chain models, with finitely extensible nonlinear elastic (FENE) spring potentials, for dilute polymeric fluids. In the models under consideration the solvent is assumed to be a compressible, isentropic, viscous, isothermal Newtonian fluid, confined to a bounded open domain in $\mathbb{R}^3$, and the velocity field is assumed to satisfy a complete slip boundary condition. We show that as the Mach number tends to zero the system is driven to its incompressible counterpart.