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Refined long-time asymptotics for some polymeric fluid flow models

Summary: Refined long-time 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
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 them in relative entropy are proved for the
linear Fokker-Planck 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


Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien


Collections: Mathematics