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Mathematics  2015 

Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data

DOI: 10.4064/ba63-1-6

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Abstract:

A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than $8\pi$ as the initial data is given. This result has been obtained by Senba--Suzuki and Bedrossian--Masmoudi using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.

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