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arXiv · 1011.0282

Measure valued solutions of the 2D Keller-Segel system

S. Luckhaus·Y. Sugiyama·J. J. L. Velázquez
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Abstract

We study the solutions of the two-dimensional Keller-Segel system describing chemotaxis. The Keller-Segel system as well as the properties of the blow-up set has been extensively studied. In this paper we obtain generalized solutions for the Keller-Segel system in the sense of measures as the limit of two-different regularizations of it. We will show that the resulting limit measures, that are in some suitable sense global weak solutions of the Keller-Segel system, depend in the regularization.

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S. Luckhaus, Y. Sugiyama, J. J. L. Velázquez. 2010-11-01. Measure valued solutions of the 2D Keller-Segel system. https://arxiv.org/abs/1011.0282

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