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arXiv · 1710.08085

The $L^2$ decay for the 2D co-rotation FENE dumbbell model of polymeric flows

Wei Luo·Zhaoyang Yin
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Abstract

In this paper we mainly study the long time behaviour of solutions to the finite extensible nonlinear elastic (FENE) dumbbell model with dimension two in the co-rotation case. Firstly, we obtain the $L^2$ decay rate of the velocity of the 2D co-rotation FENE model is $(1+t)^{-\frac{1}{2}}$ 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 \cite{Luo-Yin,Schonbek}.

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Wei Luo, Zhaoyang Yin. 2017-10-23. The $L^2$ decay for the 2D co-rotation FENE dumbbell model of polymeric flows. https://doi.org/10.1016/j.aim.2018.11.028

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