The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids

Details The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids

2010-10-27

arxiv.org/abs/1010.5807v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

The FENE dumbbell model consists of the incompressible Navier-Stokes equation and the Fokker-Planck equation for the polymer distribution. In such a model, the polymer elongation cannot exceed a limit $\sqrt{b}$, yielding all interesting features near the boundary. In this paper we establish the local well-posedness for the FENE dumbbell model under a class of Dirichlet-type boundary conditions dictated by the parameter $b$. As a result, for each $b>0$ we identify a sharp boundary requirement for the underlying density distribution, while the sharpness follows from the existence result for each specification of the boundary behavior. It is shown that the probability density governed by the Fokker-Planck equation approaches zero near boundary, necessarily faster than the distance function $d$ for $b>2$, faster than $d|ln d|$ for $b=2$, and as fast as $d^{b/2}$ for $0

Affiliated with

Also associated with

No associations

Rating

The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Cauchy-Dirichlet problem for the FENE dumbbell model of polymeric fluids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-582497