 
Summary: Refined longtime asymptotics for some
polymeric fluid flow models
A. Arnold
, J.A. Carrillo
, C. Manzini
October 5, 2009
2000 Mathematical Subject Classification: 35K15, 35Q30, 35B40; 76T20
Keywords: entropy method, relative entropy, Fokker Planck equations, large time be
havior, exponential decay rate, polymeric flow, dumbbell model
Abstract
We consider a polymeric fluid model, consisting of the incompressible Navier
Stokes equations coupled to a nonsymmetric FokkerPlanck equation. First, steady
states and exponential convergence to them in relative entropy are proved for the
linear FokkerPlanck equation in the Hookean case. The FENE model is also ad
dressed proving the existence of stationary states and the convergence towards
them in suitable weighted norms. Then, using the "entropy method" exponen
tial 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.
1 Introduction
