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 steady-state 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 co-rotation FENE model is \({(1+t)^{-\frac{d}{4}}}\) when \({d \geqq 3}\), and \({\ln^{-k}{(e+t)}, k\in \mathbb{N}^{+}}\) when d = 2. This result improves considerably the recent result of Schonbek (SIAM J Math Anal 41:564–587, 2009). Moreover, we investigate the L 2 decay of solutions to the general FENE model.
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Communicated by P. Rabinowitz
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Luo, W., Yin, Z. The Liouville Theorem and the L 2 Decay for the FENE Dumbbell Model of Polymeric Flows. Arch Rational Mech Anal 224, 209–231 (2017). https://doi.org/10.1007/s00205-016-1072-1
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DOI: https://doi.org/10.1007/s00205-016-1072-1