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Existence of Solutions for the Keller–Segel Model of Chemotaxis with Measures as Initial Data

Volume 63 / 2015

Piotr Biler, Jacek Zienkiewicz Bulletin Polish Acad. Sci. Math. 63 (2015), 41-51 MSC: 35Q92, 35B44, 35K55. DOI: 10.4064/ba63-1-6

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 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.

Authors

  • Piotr BilerInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail
  • Jacek ZienkiewiczInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland
    e-mail

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