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June 2008 The parabolic-parabolic Keller-Segel model in R2
V. Calvez, L. Corrias
Commun. Math. Sci. 6(2): 417-447 (June 2008).


This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel system in the full space. We derive a critical mass threshold below which global existence is ensured. Carefully using energy methods and ad hoc functional inequalities, we improve and extend previous results in this direction. The given threshold is thought to be the optimal criterion, but this question is still open. This global existence result is accompanied by a detailed discussion on the duality between the Onofri and the logarithmic Hardy-Littlewood-Sobolev inequalities that underlie the following approach.


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V. Calvez. L. Corrias. "The parabolic-parabolic Keller-Segel model in R2." Commun. Math. Sci. 6 (2) 417 - 447, June 2008.


Published: June 2008
First available in Project Euclid: 1 July 2008

zbMATH: 1149.35360
MathSciNet: MR2433703

Primary: 35B60 , 35Q80 , 92B05 , 92C17

Keywords: chemotaxis , Energy method , global weak solutions , Hardy-Littlewood-Sobolev inequality , Onofri inequality , parabolic system

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 2 • June 2008
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