Analysis of polymeric flow models and related compactness theorems in weighted spaces


Journal Article

We studied coupled systems of the Fokker-Planck equation and the Navier-Stokes equation modeling the Hookean and the finitely extensible nonlinear elastic (FENE)-type polymeric flows. We proved the continuous embedding and compact embedding theorems in weighted spaces that naturally arise from related entropy estimates. These embedding estimates are shown to be sharp. For the Hookean polymeric system with a center-of-mass diffusion and a superlinear spring potential, we proved the existence of a global weak solution. Moreover, we were able to tackle the FENE model with L2 initial data for the polymer density instead of the L∞ counterpart in the literature. © 2013 Society for Industrial and Applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Chen, X; Liu, JG

Published Date

  • October 4, 2013

Published In

Volume / Issue

  • 45 / 3

Start / End Page

  • 1179 - 1215

Electronic International Standard Serial Number (EISSN)

  • 1095-7111

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/120887850

Citation Source

  • Scopus