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SUMMARY:Some polymeric fluid flow models: steady states and large-time con
 vergence - Arnold\, A (TU Wien)
DTSTART:20100907T151000Z
DTEND:20100907T155000Z
UID:TALK26067@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider a dumbbell model for a dilute solution of polymers
  in a homogeneous fluid. In a micro-macro model\, the incompressible Navie
 r-Stokes equation for the fluid flow is coupled to a Fokker-Planck equatio
 n for the (microscipic) distribution of the polymeric chains. \n\nFirst we
  analyze the linear Fokker-Planck equation for Hookean dumbbells and in th
 e case of finite extension nonlinear elasticity (FENE): steady states and 
 large-time convergence using entropy methods. In the FENE case the station
 ary problem is degenerate elliptic\, requiring to use weighted Sobolev spa
 ces. In the coupled Hookean case we also show exponential convergence to a
  homogeneous stationary flow. \n\nReferences: A. Arnold\, J.A. Carrillo\, 
 C. Manzini: Refined long-time asymptotics for some polymeric fluid flow mo
 dels\, Comm. Math. Sc. 8\, No. 3 (2010) 763-782. \n\nA. Arnold\, C. Bardos
 \, I. Catto: Stable steady states of a FENE-dumbbell model for polymeric f
 luid flows\, preprint\, 2010. \n
LOCATION:Seminar Room 1\, Newton Institute
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