Well-posedness and Gevrey Analyticity of the Generalized Keller-Segel System in Critical Besov Spaces

2015/08/01 by Jihong Zhao, Zhao, Jihong · 1 citation
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · #35B65 #35K15 #35M11 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1508.00117

openalex publication_date 2015/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the Cauchy problem for the generalized Keller-Segel system with the cell diffusion being ruled by fractional diffusion: \begincases ∂_tu+Λ^αu-∇⋅(u∇ ψ)=0 amp;in ℝⁿ×(0,∞), -Δψ=u amp;in ℝⁿ×(0,∞), u(x,0)=u₀(x), amp;in ℝⁿ. \endcases In the case that 1

Citations

• On explosions of solutions to a system of partial differential equations modelling chemotaxis
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Optimal criteria for blowup of radial and N-symmetric solutions of\n chemotaxis systems

Cited by

• Time-refined Triebel--Lizorkin Estimates and Applications to Keller--Segel Type Equations

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