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引用次数: 3
摘要
We give a simple proof, relying on a two-particles moment computation, that there exists a global weak solution to the \begin{document}$ 2 $\end{document}-dimensional parabolic-elliptic Keller-Segel equation when starting from any initial measure \begin{document}$ f_0 $\end{document} such that \begin{document}$ f_0( {\mathbb{R}}^2)< 8 \pi $\end{document}.
A simple proof of non-explosion for measure solutions of the Keller-Segel equation
We give a simple proof, relying on a two-particles moment computation, that there exists a global weak solution to the \begin{document}$ 2 $\end{document}-dimensional parabolic-elliptic Keller-Segel equation when starting from any initial measure \begin{document}$ f_0 $\end{document} such that \begin{document}$ f_0( {\mathbb{R}}^2)< 8 \pi $\end{document}.
期刊介绍：
KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.
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