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A Note on the Subcritical Two Dimensional Keller-Segel System

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Abstract

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).

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Authors and Affiliations

  1. ICREA and Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra (Barcelona), 08193, Spain

    Jose A. Carrillo

  2. Department of Mathematical Sciences, Tsinghua University, Bei**g, 100084, P.R. China

    Li Chen & **huan Wang

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

    Jian-Guo Liu

  4. Department of Mathematics, Liaoning University, Shenyang, 110036, P.R. China

    **huan Wang

Authors
  1. Jose A. Carrillo
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  2. Li Chen
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  3. Jian-Guo Liu
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  4. **huan Wang
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Corresponding author

Correspondence to Jose A. Carrillo.

Additional information

J.A. Carrillo is partially supported by the project MTM2011-27739-C04 DGI-MCI (Spain) and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. L. Chen is partially supported by National Natural Science Foundation of China (NSFC) grant 10871112, 11011130029. The research of J.-G. Liu was partially supported by NSF grant DMS 10-11738. J. Wang is partially supported by Science Foundation of Liaoning Education Department grant L2010146 and China Postdoctoral Science Foundation grant 20110490409. J.-G. Liu wish to acknowledge the hospitality of Mathematical Sciences Center of Tsinghua University where part of this research was performed.

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Carrillo, J.A., Chen, L., Liu, JG. et al. A Note on the Subcritical Two Dimensional Keller-Segel System. Acta Appl Math 119, 43–55 (2012). https://doi.org/10.1007/s10440-011-9660-4

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  • DOI: https://doi.org/10.1007/s10440-011-9660-4

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