Refined long-time asymptotics for some polymeric fluid flow models

A. Arnold, J. A. Carrillo, C. Manzini

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)

Abstract

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. © 2010 International Press.
Original languageEnglish
Pages (from-to)763-782
JournalCommunications in Mathematical Sciences
Volume8
Issue number3
DOIs
Publication statusPublished - 1 Jan 2010

Keywords

  • Dumbbell model
  • Entropy method
  • Exponential decay rate
  • Fokker-Planck equations
  • Large time behavior
  • Polymeric flow
  • Relative entropy

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