Periodic long-time behaviour for an approximate model of nematic polymers

TL;DR

This paper investigates the long-term dynamics of a nonlinear Fokker-Planck model for nematic polymers, deriving the Doi closure microscopically and demonstrating convergence to periodic solutions over time.

Contribution

It provides a microscopic derivation of the Doi closure and proves convergence of solutions to periodic states in the long-time limit.

Findings

Derivation of the Doi closure from microscopic principles

Proof of convergence to periodic solutions

Insights into the long-time behaviour of nematic polymer models

Abstract

We study the long-time behaviour of a nonlinear Fokker-Planck equation, which models the evolution of rigid polymers in a given flow, after a closure approximation. The aim of this work is twofold: first, we propose a microscopic derivation of the classical Doi closure, at the level of the kinetic equation ; second, we prove the convergence of the solution to the Fokker-Planck equation to periodic solutions in the long-time limit.