Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : The KellerSegel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form it is a conservative driftdiffusion equation for the cell density coupled to an elliptic equation for the chemoattractant concentration. It is known that, in two space dimensions, for small initial mass there is global existence of classical solutions and for large initial mass blowup occurs. In this note we complete this picture and give an explicit value for the critical mass when the system is set in the whole space. 





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