Geodesic
Existence of Solutions for the Keller–Segel Model of Chemotaxis with Measures as Initial Data
Piotr Biler1 ; Jacek Zienkiewicz1
1 Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 63 (2015) no. 1, pp. 41-51

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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 $8\pi $ 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.
DOI : 10.4064/ba63-1-6
Keywords: simple proof existence solutions two dimensional keller segel model measures atoms initial given result obtained senba suzuki bedrossian masmoudi using different arguments moreover uniform bound existence time solutions optimal hypercontractivity estimate

Piotr Biler 1 ; Jacek Zienkiewicz 1

1 Instytut Matematyczny Uniwersytet Wrocławski Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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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) no. 1, pp. 41-51. doi: 10.4064/ba63-1-6

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