Local criteria for blowup in two-dimensional chemotaxis models

2014/10/28 by Biler, Piotr, Cieślak, Tomasz, Karch, Grzegorz +1 · 1 citation
#35B44 #35K55 #35Q92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.7807

Abstract

We consider two-dimensional versions of the Keller--Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solutions in terms of suitable Morrey spaces norms are derived. Moreover, the impact of the consumption term on the global-in-time existence of solutions is analyzed for the classical Keller--Segel system.

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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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