The parabolic-parabolic Keller-Segel model in R2

被引：3

作者：

Calvez, Vincent ^{[1
]}

Corrias, Lucilla ^{[2
]}

机构：

[1] ENS, CNRS, Dept Math & Applicat, UMR8553, F-75230 Paris 05, France

[2] Univ Evry Val Essonne, Dept Math, F-91025 Evry, France

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2008年 / 6卷 / 02期

关键词：

chemotaxis; parabolic system; global weak solutions; energy method; Onofri inequality; Hardy-Littlewood-Sobolev inequality;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：417 / 447

页数：31

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