Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data
Piotr Biler ; Jacek Zienkiewicz
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015), p. 41-51 / Harvested from The Polish Digital Mathematics Library
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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 was obtained by Senba and Suzuki (2002) and Bedrossian and Masmoudi (2014) using different arguments. Moreover, we show a uniform bound for the existence time of solutions as well as an optimal hypercontractivity estimate.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:281224 
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     title = {Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
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     year = {2015},
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Piotr Biler; Jacek Zienkiewicz. Existence of Solutions for the Keller-Segel Model of Chemotaxis with Measures as Initial Data. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) pp. 41-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba63-1-6/