Analysis of Polymeric Flow Models and Related CompactnessTheorems in Weighted Spaces

CHEN Xiuqing; LIU Jianguo

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Analysis of Polymeric Flow Models and Related CompactnessTheorems in Weighted Spaces

CHEN Xiuqing 1 *,LIU Jianguo 2

1.School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876

2.Department of Physics and Department of Mathematics, Duke University, Durham, NC 27708 USA

*Correspondence author

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Funding: National Science Foundation （NSF）of the USA（No.grant DMS 10-11738）, the Research Fund for the Doctoral Programof Higher Education of China（No.grant 20090005120009）, National Science Foundation of China （No.grant 11101049）

Opened online:27 August 2012

Accepted by: none

Citation: CHEN Xiuqing,LIU Jianguo.Analysis of Polymeric Flow Models and Related CompactnessTheorems in Weighted Spaces[OL]. [27 August 2012] http://en.paper.edu.cn/en_releasepaper/content/4487223

This paper investigates a coupledsystem of Fokker-Planck equation and Navier-Stokes equation modelingHookean and FENE type polymeric flows. Some continuous andcompact embedding theorems in weighted spaces naturally arising fromrelative entropy estimate are proved. Those embedding theorems are shown to besharp. For Hookean polymeric system with center-of-mass diffusionand super-linear spring potential, the existence of globalweak solution is obtained. Moreover, the FENE model with L2 initial data for the density of polymer instead of L∞ counterpart in the existent literature can be tackled.

Keywords:Fokker-Planckequation; Navier-Stokes equation; compact embeddingtheorem; logarithmic Sobolev inequality; Hardy-tpe inequality

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