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Title of Journal: Arch Rational Mech Anal

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Abbravation: Archive for Rational Mechanics and Analysis

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Springer Berlin Heidelberg

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10.1007/bf00010006

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1432-0673

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The Liouville Theorem and the Emphasis Type="Ital

Authors: Wei Luo Zhaoyang Yin
Publish Date: 2016/12/29
Volume: 224, Issue: 1, Pages: 209-231
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Abstract

In this paper we mainly study the finite extensible nonlinear elastic FENE dumbbell model with dimension d geqq 2 in the whole space We first prove that there is only the trivial solution for the steadystate FENE model under some integrable condition The obtained results generalize and cover the classical results for the stationary Navier–Stokes equations We then obtain that the L 2 decay rate of the velocity of the corotation FENE model is 1+tfracd4 when d geqq 3 and lnke+t kin mathbbN+ when d = 2 This result improves considerably the recent result of Schonbek SIAM J Math Anal 41564–587 2009 Moreover we investigate the L 2 decay of solutions to the general FENE model


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