The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation

TL;DR

This paper proves the existence and uniqueness of solutions for the coupled Navier-Stokes and Fokker-Planck equations in the FENE dumbbell polymer model, under certain initial conditions and assumptions.

Contribution

It establishes global well-posedness results for the FENE model in 2D bounded domains, including the corotational case, with specific initial data conditions.

Findings

Global existence and uniqueness of solutions in 2D bounded domains.

Conditions on initial data for well-posedness.

Results applicable to corotational case with less restrictive initial data.

Abstract

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coeffcients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.