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September 2010 Refined long-time asymptotics for some polymeric fluid flow models
A. Arnold, J. A. Carrillo, C. Manzini
Commun. Math. Sci. 8(3): 763-782 (September 2010).


We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, the existence of steady states and the exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed, and the proof of the existence of stationary states and the convergence towards them in suitable weighted norms is given. Then, using the “entropy method” exponential convergence to the steady state is established for the coupled model in the Hookean case under some smallness assumption. The results continue and expand the analysis of B. Jourdain, C. Le Bris, T. Lelièvre and F. Otto, Arch. Rational Mech. Anal., 181, 97-148, 2006 in both the Hookean and the FENE models.


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A. Arnold. J. A. Carrillo. C. Manzini. "Refined long-time asymptotics for some polymeric fluid flow models." Commun. Math. Sci. 8 (3) 763 - 782, September 2010.


Published: September 2010
First available in Project Euclid: 25 August 2010

zbMATH: 1213.35094
MathSciNet: MR2730330

Primary: 35B40 , 35K15 , 35Q30 , 76T20

Keywords: dumbbell model , entropy method , exponential decay rate , Fokker-Planck equations , Large time behavior , polymeric flow , Relative entropy

Rights: Copyright © 2010 International Press of Boston

Vol.8 • No. 3 • September 2010
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