Existence of Solutions for the Keller–Segel Model of Chemotaxis with Measures as Initial Data

DOI10.4064/ba63-1-6zbMath1326.35399arXiv1507.00497OpenAlexW3098516952MaRDI QIDQ2949780

Piotr Biler, Jacek Zienkiewicz

Publication date: 2 October 2015

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.00497

zbMATH Keywords

chemotaxisblow-up of solutions

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Cell movement (chemotaxis, etc.) (92C17) Blow-up in context of PDEs (35B44)

Related Items (12)

A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation ⋮ Large global-in-time solutions to a nonlocal model of chemotaxis ⋮ Global existence of free-energy solutions to the 2D Patlak-Keller-Segel-Navier-Stokes system with critical and subcritical mass ⋮ Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis ⋮ Does strong repulsion lead to smooth solutions in a repulsion-attraction chemotaxis system even when starting with highly irregular initial data? ⋮ On the existence of global smooth solutions to the parabolic-elliptic Keller-Segel system with irregular initial data ⋮ The full Keller–Segel model is well-posed on nonsmooth domains ⋮ Local criteria for blowup in two-dimensional chemotaxis models ⋮ Keller-Segel chemotaxis models: a review ⋮ Mathematical challenges in the theory of chemotaxis ⋮ Global radial solutions in classical Keller-Segel model of chemotaxis ⋮ Morrey spaces norms and criteria for blowup in chemotaxis models

Cites Work

• Existence, uniqueness and Lipschitz dependence for Patlak-Keller-Segel and Navier-Stokes in \(\mathbb R^2\) with measure-valued initial data
• Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis
• Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane
• Two-dimensional Navier-Stokes flow with measures as initial vorticity
• Symmetrization techniques on unbounded domains: Application to a chemotaxis system on \(\mathbb{R}^N\)
• Weak solutions to a parabolic-elliptic system of chemotaxis
• Optimal criteria for blowup of radial andN-symmetric solutions of chemotaxis systems
• The Cauchy problem and self-similar solutions for a nonlinear parabolic equation
• Chemotactic collapse in a parabolic-elliptic system of mathematical biology
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