Refined hyper-contractivity and uniqueness for the Keller-Segel equations

Jian-Guo Liu Duke University Jinhuan Wang Liaoning University

Analysis of PDEs mathscidoc:1702.03028

Applied Mathematics Letters, 52, 212–219, 2016.2
This note considers the hyper-contractivity and the uniqueness of the weak solutions to the two dimensional Keller–Segel equations. We prove a refined hyper-contractive property and consequently obtain the uniqueness of global weak solutions provided that the initial data satisfy , and . We also extend the result to higher dimensions.
Hyper-contractivity Uniqueness LlogL space Semi-group theory
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@inproceedings{jian-guo2016refined,
  title={Refined hyper-contractivity and uniqueness for the Keller-Segel equations},
  author={Jian-Guo Liu, and Jinhuan Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207231349181490273},
  booktitle={Applied Mathematics Letters},
  volume={52},
  pages={212–219},
  year={2016},
}
Jian-Guo Liu, and Jinhuan Wang. Refined hyper-contractivity and uniqueness for the Keller-Segel equations. 2016. Vol. 52. In Applied Mathematics Letters. pp.212–219. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170207231349181490273.
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