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A. Arnold, J. Carrillo, C. Manzini:
"Refined long-time asymptotics for some polymeric fluid flow models";
in: "ASC Report 07/2009", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2009, ISBN: 978-3-902627-02-5.

We consider a polymeric fluid model, consisting of the incompressible Navier-
Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady
states and exponential convergence to it in relative entropy are proved for the linear
Fokker-Planck equation in the Hookean case. The FENE model is also addressed
proving the existence of stationary states and the convergence towards them in
suitable weighted norms. 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 [JLLO] in both the Hookean and the FENE models.

http://www.asc.tuwien.ac.at/preprint/2009/asc07x2009.pdf