Quantitative analysis and its applications for Keller-Segel type systems

2024/06/12 by Ding, Mengyao, Fang, Yuzhou, Zhang, Chao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.07982

Abstract

In this paper, we utilize the De Giorgi iteration to quantitatively analyze the upper bound of solutions for Keller-Segel type systems. The refined upper bound estimate presented here has broad applications in determining large time behaviours of weak solutions and improving the regularity for models involving the p-Laplace operator. To demonstrate the applicability of our findings, we investigate the asymptotic stability of a chemotaxis model with nonlinear signal production and a chemotaxis-Navier-Stokes model with a logistic source. Additionally, within the context of p-Laplacian diffusion, we establish Hölder continuity for a chemotaxis-haptotaxis model and a chemotaxis-Stokes model.

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