Existence of Solutions for the Keller–Segel Model of Chemotaxis with Measures as Initial Data
Tom 63 / 2015
Bulletin Polish Acad. Sci. Math. 63 (2015), 41-51 MSC: 35Q92, 35B44, 35K55. DOI: 10.4064/ba63-1-6
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.