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arXiv · 1507.00497

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

Piotr Biler·Jacek Zienkiewicz
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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 $8π$ 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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Piotr Biler, Jacek Zienkiewicz. 2015-10-17. Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data. https://doi.org/10.4064/ba63-1-6

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