Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces
type: Item
instance of: scholarly article
title: Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces
zbMATH Open document ID: 1483.35290
author: Takeshi Suguro
published in: Journal of Evolution Equations
publication date: 2022-01-06T00:00:00Z
review text: The parabolic-elliptic Keller-Segel system is studied in the whole space \(\mathbb R^n\) in the scale of uniformly local Lebesgue spaces with exponents \(r\ge n/2\). Results on local well-posedness and global-in-time well-posedness for small initial data are shown. Estimates of Bessel potentials are the key point of the analysis. The case \(r=n/2\) extends recent work [\textit{S. Cygan} et al., J. Evol. Equ. 21, No. 4, 4873--4896 (2021; Zbl 1487.35056)].
reviewed by: Piotr Biler
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 7452682
zbMATH Keywords: parabolic-elliptic Keller-Segel system
zbMATH Keywords: uniformly local Lebesgue spaces
zbMATH Keywords: Bessel potentials
zbMATH Keywords: mild solutions
zbMATH Keywords: well-posedness
MaRDI profile type: Publication
full work available at URL: s00028-021-00727-w
OpenAlex ID: W3168906959
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DOI: 10.1007/S00028-021-00727-W
description: scientific article; zbMATH DE number 7452682