Abstract
In this paper we mainly study the long time behavior of solutions to the finite extensible nonlinear elastic (FENE) dumbbell model with dimension two in the co-rotation case. Firstly, we obtain the L2 decay rate of the velocity of the 2D co-rotation FENE model is (1+t)−12 with small data. Then, by virtue of the Littlewood–Paley theory, we can remove the small condition. Our obtained sharp result improves considerably the recent results in [8,14].
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