| Contents |
| This talk is dedicated to recent results on the Keller-Segel model in
2d, and on its variants in higher dimensions where the diffusion is of
critical porous medium type. These models have a critical mass $M_c$
such that the solutions exist globally in time if the mass is less than
$M_c$ and above which there are solutions which blowup in finite time.
The main tools, in particular the free energy and the
Jordan-Kinderlherer-Otto's minimising scheme in the Monge-Kantorovich
metric, and the idea of the methods are set out. |
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