Large time behavior to the FENE dumbbell model of polymeric flows near equilibrium

TL;DR

This paper investigates the long-term decay behavior of solutions to the FENE dumbbell model of polymeric flows, establishing an optimal decay rate for velocity in the general case, extending previous results.

Contribution

It proves the optimal $L^2$ decay rate of velocity for the FENE model in the general case, improving prior results for the co-rotation model.

Findings

Optimal $L^2$ decay rate of $(1+t)^{-rac{d}{4}}$ for velocity

Extension of decay results to the general FENE model case

Improvement over previous decay rate estimates

Abstract

In this paper we mainly study large time behavior for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. There is a lot results about the $L^2$ decay rate of the co-rotation model. In this paper, we consider the general case. We prove that the optimal $L^2$ decay rate of the velocity is $(1+t)^{-\frac{d}{4}}$ with $d\geq 2$. This result improves the previous result in \cite{Luo-Yin}.