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A note on the subcritical two dimensional Keller-Segel system

Jose A. Carrillo Universitat Autònoma de Barcelona Li Chen Tsinghua University Jian-Guo Liu Duke University Jinhuan Wang Liaoning University

Analysis of PDEs mathscidoc:1702.03050

Acta Applicandae Mathematicae, 119, (1), 43-55, 2012.6
The existence of solution for the 2D-Keller-Segel system in the subcritical case, i.e. when the initial mass is less than 8π, is reproved. Instead of using the entropy in the free energy and free energy dissipation, which was used in the proofs (Blanchet et al. in SIAM J. Numer. Anal. 46:691–721, 2008; Electron. J. Differ. Equ. Conf. 44:32, 2006 (electronic)), the potential energy term is fully utilized by adapting Delort’s theory on 2D incompressible Euler equation (Delort in J. Am. Math. Soc. 4:553–386, 1991).
Chemotaxis·Critical mass· Global existence · Maximal density function
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@inproceedings{jose2012a,
  title={A note on the subcritical two dimensional Keller-Segel system},
  author={Jose A. Carrillo, Li Chen, Jian-Guo Liu, and Jinhuan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208225603972573331},
  booktitle={Acta Applicandae Mathematicae},
  volume={119},
  number={1},
  pages={43-55},
  year={2012},
}
Jose A. Carrillo, Li Chen, Jian-Guo Liu, and Jinhuan Wang. A note on the subcritical two dimensional Keller-Segel system. 2012. Vol. 119. In Acta Applicandae Mathematicae. pp.43-55. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170208225603972573331.
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