Maximal Lorentz regularity for the Keller-Segel system of parabolic-elliptic type
type: Item
instance of: scholarly article
title: Maximal Lorentz regularity for the Keller-Segel system of parabolic-elliptic type
zbMATH Open document ID: 1482.35231
author: Taiki Takeuchi
published in: Journal of Evolution Equations
publication date: 2022-01-06T00:00:00Z
review text: The minimal parabolic-elliptic Keller-Segel system is studied in the whole space \(\mathbb R^n\), \(n\ge 2\), in the homogeneous Besov spaces \(\dot B^{-2+n/p}_{p,q}\) which are scale-invariant. The concept of the maximal parabolic Lorentz regularity in time is systematically applied to construct solutions with \(u_t,\, \Delta u\in L^{\alpha,q}((0,\infty);\dot B^s_{r,1}(\mathbb R^n))\) for \(2/\alpha+n/r=4+s\), \(1\le q\le \infty\). Local solutions are constructed as well as global-in-time ones for small initial data.
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 7452683
zbMATH Keywords: chemotaxis
zbMATH Keywords: maximal regularity
zbMATH Keywords: Besov space
MaRDI profile type: Publication
full work available at URL: s00028-021-00728-9
OpenAlex ID: W3168326844
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DOI: 10.1007/S00028-021-00728-9
description: scientific article; zbMATH DE number 7452683