A note on the subcritical two dimensional Keller-Segel system

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

doi:10.1007/s10440-011-9660-4

A note on the subcritical two dimensional Keller-Segel system

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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 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 language	English
Pages (from-to)	43-55
Journal	Acta Applicandae Mathematicae
Volume	119
Issue number	1
DOIs	https://doi.org/10.1007/s10440-011-9660-4
Publication status	Published - 1 Jun 2012

Keywords

Chemotaxis
Critical mass
Global existence
Maximal density function

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10.1007/s10440-011-9660-4

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AU - Carrillo, Jose A.

AU - Chen, Li

AU - Liu, Jian Guo

AU - Wang, Jinhuan

PY - 2012/6/1

Y1 - 2012/6/1

N2 - 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.

AB - 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.

KW - Chemotaxis

KW - Critical mass

KW - Global existence

KW - Maximal density function

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SN - 0167-8019

VL - 119

SP - 43

EP - 55

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

IS - 1

ER -

A note on the subcritical two dimensional Keller-Segel system

Abstract

Keywords

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