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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, under specific assumptions on the parameters and the initial condition, we prove convergence of the solution to the Fokker-Planck equation to a particular periodic solution in the long-time limit. © American Institute of Mathematical Sciences.

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