Well-posedness for the FENE dumbbell model of polymetric flows in Besov spaces

TL;DR

This paper establishes local and global well-posedness results for the FENE dumbbell model of polymeric flows in Besov spaces, using Littlewood-Paley theory and blow-up criteria, extending recent findings.

Contribution

It proves local well-posedness, a blow-up criterion, and global existence for the FENE model in Besov spaces, generalizing recent results in the field.

Findings

Local well-posedness in Besov spaces

Blow-up criterion for the model

Global existence near equilibrium

Abstract

In this paper we mainly investigate the Cauchy problem of the finite extensible nonlinear elastic (FENE) dumbbell model with dimension $d\geq2$. We first proved the local well-posedness for the FENE model in Besov spaces by using the Littlewood-Paley theory. Then by an accurate estimate we get a blow-up criterion. Moreover, if the initial data is perturbation around equilibrium, we obtain a global existence result. Our obtained results generalize recent results in [8].