Refined long-time asymptotics for some polymeric fluid flow models

We consider a polymeric fluid model, consisting of the incompressible NavierStokes 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 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.

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