A simple proof of non-explosion for measure solutions of the Keller-Segel equation

2022/02/07 by Nicolas Fournier, Fournier, Nicolas, Yoan Tardy +1 · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Mathematical Biology Tumor Growth #Gene Regulatory Network Analysis #Cancer Genomics and Diagnostics

paper · pdf · doi:10.48550/arxiv.2202.03508

Abstract

We give a simple proof, relying on a \it two-particles moment computation, that there exists a global weak solution to the 2-dimensional parabolic-elliptic Keller-Segel equation when starting from any initial measure f₀ such that f₀(ℝ²)< 8 π.

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• Revisiting the blow-up criterion and the maximal existence time for solutions of the parabolic-elliptic Keller-Segel system in 2d-Euclidean space

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