A note on the subcritical two dimensional Keller-Segel system

Jose A. Carrillo, Li Chen, Jian Guo Liu, Jinhuan Wang

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

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). © 2011 Springer Science+Business Media B.V.
Original languageEnglish
Pages (from-to)43-55
JournalActa Applicandae Mathematicae
Volume119
Issue number1
DOIs
Publication statusPublished - 1 Jun 2012

Keywords

  • Chemotaxis
  • Critical mass
  • Global existence
  • Maximal density function

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