On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 8, 26 p.

This review is dedicated to recent results on the 2d parabolic-elliptic Patlak-Keller-Segel model, and on its variant in higher dimensions where the diffusion is of critical porous medium type. Both of 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 idea of the methods are set out. A number of open questions are also stated.

DOI : 10.5802/slsedp.6
Blanchet, Adrien 1

1 Toulouse School of Economics (GREMAQ, Université de Toulouse) 21 Allée de Brienne F-31000 Toulouse France
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Blanchet, Adrien. On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exposé no. 8, 26 p. doi : 10.5802/slsedp.6. http://archive.numdam.org/articles/10.5802/slsedp.6/

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