Abstract
We are interested in the two-dimensional Keller–Segel partial differential equation. This equation is a model for chemotaxis (and for Newtonian gravitational interaction). When the total mass of the initial density is one, it is known to exhibit blow-up in finite time as soon as the sensitivity
In the very subcritical case
We also show that for any
Finally, we remark that in the system with
Citation
Nicolas Fournier. Benjamin Jourdain. "Stochastic particle approximation of the Keller–Segel equation and two-dimensional generalization of Bessel processes." Ann. Appl. Probab. 27 (5) 2807 - 2861, October 2017. https://doi.org/10.1214/16-AAP1267
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