Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces
type: Item
instance of: scholarly article
title: Global existence and large time behavior of a 2D Keller-Segel system in logarithmic Lebesgue spaces
zbMATH Open document ID: 1429.35030
author: Chao Deng
author: Tong Li
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2018-12-28T00:00:00Z
review text: The authors study existence of solutions for the parabolic-parabolic Keller-Segel system of chemotaxis in the whole plane. They construct global-in-time solutions for small initial data \((u_0,v_0)\) in \(L^1\times L^\infty\), as well as for data such that \(\sup_{t>0}\|\log(\mathrm{e}+t)\mathrm{e}^{t\Delta}u_0\|_\infty<\infty\) and \(v_0\in L^\infty\), both small enough. The large time behavior of such solutions is determined.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35K52
Mathematics Subject Classification ID: 35K59
Mathematics Subject Classification ID: 92C17
zbMATH DE Number: 6997059
zbMATH Keywords: global-in-time well-posedness
zbMATH Keywords: logarithmic Lebesgue spaces
MaRDI profile type: Publication
full work available at URL: dcdsb.2018093
OpenAlex ID: W2790462510
cites work: Q3431715
cites work: The parabolic-parabolic Keller-Segel model in \(\mathbb R^2\)
cites work: Nonlinear aspects of chemotaxis
cites work: A chemotaxis model motivated by angiogenesis
cites work: Global solutions of some chemotaxis and angiogenesis system in high space dimension
cites work: Symmetrization techniques on unbounded domains: Application to a chemotaxis system on \(\mathbb{R}^N\)
cites work: Well-posedness of a 3D parabolic-hyperbolic Keller-Segel system in the Sobolev space framework
cites work: Pattern formation. I: The Keller-Segel model
cites work: From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
cites work: On asymptotic behaviors of solutions to parabolic systems modelling chemotaxis
cites work: Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
cites work: Initiation of slime mold aggregation viewed as an instability
cites work: Model for chemotaxis
cites work: Traveling bands of chemotactic bacteria: a theoretical analysis
cites work: Global strong solution to the semi-linear Keller-Segel system of parabolic-parabolic type with small data in scale invariant spaces
cites work: The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions
cites work: Existence and uniqueness theorem on mild solutions to the Keller-Segel system in the scaling invariant space
cites work: Q4782579
cites work: A System of Reaction Diffusion Equations Arising in the Theory of Reinforced Random Walks
cites work: ON A HYPERBOLIC–PARABOLIC SYSTEM MODELING CHEMOTAXIS
cites work: Global dynamics of a hyperbolic-parabolic model arising from chemotaxis
cites work: Nonlinear Stability of Traveling Waves to a Hyperbolic-Parabolic System Modeling Chemotaxis
cites work: Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis
cites work: Large amplitude stationary solutions to a chemotaxis system
cites work: Traveling waves in a chemotactic model
cites work: Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks
cites work: Random walk with persistence and external bias
cites work: The Existence and Stability of Spike Patterns in a Chemotaxis Model
cites work: Shock formation in a chemotaxis model
cites work: Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
cites work: The solvability of some chemotaxis systems
DOI: 10.3934/DCDSB.2018093
description: scientific article; zbMATH DE number 6997059