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Analysis of PDEsmathscidoc:1702.03042

Siam Journal on Mathematical Analysis, 45, (3), 1179–1215, 2013.5
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 $L^2$ initial data for the polymer density instead of the $L^\infty$ counterpart in the literature.
Fokker–Planck equation, Navier–Stokes equation, polymer, compact embedding theorem, logarithmic Sobolev inequality, Hardy-type inequality, Hookean
@inproceedings{xiuqing2013analysis,
title={Analysis of polymeric flow models and related compactness theorems in weighted spaces},
author={XIUQING CHEN, and Jian-Guo Liu},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208220556558895319},
booktitle={Siam Journal on Mathematical Analysis},
volume={45},
number={3},
pages={1179–1215},
year={2013},
}

XIUQING CHEN, and Jian-Guo Liu. Analysis of polymeric flow models and related compactness theorems in weighted spaces. 2013. Vol. 45. In Siam Journal on Mathematical Analysis. pp.1179–1215. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208220556558895319.