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Acta Applicandae Mathematicae

, Volume 119, Issue 1, pp 43–55 | Cite as

A Note on the Subcritical Two Dimensional Keller-Segel System

  • Jose A. CarrilloEmail author
  • Li Chen
  • Jian-Guo Liu
  • Jinhuan Wang
Article

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).

Keywords

Chemotaxis Critical mass Global existence Maximal density function 

Mathematics Subject Classification (2000)

35K55 35B33 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Jose A. Carrillo
    • 1
    Email author
  • Li Chen
    • 2
  • Jian-Guo Liu
    • 3
  • Jinhuan Wang
    • 2
    • 4
  1. 1.ICREA and Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra (Barcelona)Spain
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingP.R. China
  3. 3.Department of Physics and Department of MathematicsDuke UniversityDurhamUSA
  4. 4.Department of MathematicsLiaoning UniversityShenyangP.R. China

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