70 research outputs found
Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data
A simple proof of the existence of solutions for the two-dimensional
Keller-Segel model with measures with all the atoms less than 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
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