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Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions

Xiuqing Chen Beijing University of Posts and Telecommunications Jian-Guo Liu Duke University

Analysis of PDEs mathscidoc:1702.03044

Journal of Differential Equations, 254, (7), 2764–2802, 2013.4
We prove the existence of the global weak entropy solution to the Doi–Saintillan–Shelley model for active and passive rod-like particle suspensions, which couples a Fokker–Planck equation with the incompressible Navier–Stokes or Stokes equation, under the no-flux boundary conditions, L2(Ω;L1(Sd611))L2(Ω;L1(Sd611)) initial data, and finite initial entropy for the particle distribution function in two and three dimensions. Furthermore, for the model with the Stokes equation, we obtain the global L2(Ω×Sd611)L2(Ω×Sd611) weak solution in two and three dimensions and the uniqueness in two dimension.
Rod-like particle suspensions Global entropy solution Uniqueness Fokker–Planck equation Navier–Stokes equation No-flux boundary condition
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@inproceedings{xiuqing2013global,
  title={Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions},
  author={Xiuqing Chen, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208222339161577322},
  booktitle={Journal of Differential Equations},
  volume={254},
  number={7},
  pages={2764–2802},
  year={2013},
}
Xiuqing Chen, and Jian-Guo Liu. Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions. 2013. Vol. 254. In Journal of Differential Equations. pp.2764–2802. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208222339161577322.
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