On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher
Blanchet, Adrien
arXiv, 1109.1543 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2011-09-07
Classification:  Mathematics - Analysis of PDEs 
@article{1109.1543,
     author = {Blanchet, Adrien},
     title = {On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and
  higher},
     journal = {arXiv},
     volume = {2011},
     number = {0},
     year = {2011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1109.1543}
}

Blanchet, Adrien. On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and
  higher. arXiv, Tome 2011 (2011) no. 0, . http://gdmltest.u-ga.fr/item/1109.1543/