Global existence of weak solutions to the FENE dumbbell model of polymeric flows

TL;DR

This paper proves the global existence of weak solutions for the FENE dumbbell model of polymeric flows, addressing complex nonlinear terms through advanced weak convergence techniques.

Contribution

It establishes the global existence of weak solutions for a broad class of potentials in the FENE model, using novel weak convergence methods.

Findings

Proved global existence of weak solutions.

Developed techniques for handling nonlinear terms without obvious compactness.

Extended results to a very general class of potentials.

Abstract

Systems coupling fluids and polymers are of great interest in many branches of sciences. One of the models to describe them is the FENE (Finite Extensible Nonlinear Elastic) dumbbell model. We prove global existence of weak solutions to the FENE dumbbell model of polymeric flows for a very general class of potentials. The main problem is the passage to the limit in a nonlinear term that has no obvious compactness properties. The proof uses many weak convergence techniques. In particular it is based on the control of the propagation of strong convergence of some well chosen quantity by studying a transport equation for its defect measure.