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

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 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.

Cited by in corpus (3)

• On the existence of global smooth solutions to the parabolic-elliptic Keller-Segel system with irregular initial data
• Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis
• The full Keller-Segel model is well-posed on nonsmooth domains