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.
Publié le : 2008-06-15
Classification:
chemotaxis,
parabolic system,
global weak solutions,
energy method,
Onofri inequality,
Hardy-Littlewood-Sobolev inequality,
35B60,
35Q80,
92C17,
92B05
@article{1214949930,
author = {Calvez, V. and Corrias, L.},
title = {The parabolic-parabolic Keller-Segel model in R2},
journal = {Commun. Math. Sci.},
volume = {6},
number = {1},
year = {2008},
pages = { 417-447},
language = {en},
url = {http://dml.mathdoc.fr/item/1214949930}
}
Calvez, V.; Corrias, L. The parabolic-parabolic Keller-Segel model in R2. Commun. Math. Sci., Tome 6 (2008) no. 1, pp. 417-447. http://gdmltest.u-ga.fr/item/1214949930/