Global well-posedness and blow-up for the 2-D Patlak-Keller-Segel equation

DOI10.1016/j.jfa.2017.10.019zbMath1380.35031OpenAlexW2766680942MaRDI QIDQ1677451

Dongyi Wei

Publication date: 21 November 2017

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2017.10.019

zbMATH Keywords

mild solutionsmonotonicity formulasnonnegative integrable data

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Continuation and prolongation of solutions to PDEs (35B60) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)

Related Items (16)

A double critical mass phenomenon in a no-flux-Dirichlet Keller-Segel system ⋮ Unnamed Item ⋮ Global existence of free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass ⋮ Classical solutions to Cauchy problems for parabolic-elliptic systems of Keller-Segel type ⋮ Global existence of solutions to the 4D attraction–repulsion chemotaxis system and applications of Brezis–Merle inequality ⋮ Corners and collapse: some simple observations concerning critical masses and boundary blow-up in the fully parabolic Keller-Segel system ⋮ Critical mass for Keller–Segel systems with supercritical nonlinear sensitivity ⋮ A simple proof of non-explosion for measure solutions of the Keller-Segel equation ⋮ Global regularity and stability analysis of the Patlak-Keller-Segel system with flow advection in a bounded domain: a semigroup approach ⋮ Finite-time blow-up in the Cauchy problem of a Keller-Segel system with logistic source ⋮ Enhanced Dissipation and Blow-Up Suppression in a Chemotaxis-Fluid System ⋮ Global solutions of aggregation equations and other flows with random diffusion ⋮ Unnamed Item ⋮ Global existence of solutions to a two dimensional attraction-repulsion chemotaxis system in the attractive dominant case with critical mass ⋮ Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO} ⋮ Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions

Cites Work

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• Point Dynamics in a Singular Limit of the Keller--Segel Model 2: Formation of the Concentration Regions
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