Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces
type: Item
instance of: scholarly article
title: Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces
zbMATH Open document ID: 1402.35212
published in: Science China. Mathematics
publication date: 2018-03-07T00:00:00Z
review text: The authors study a system of partial differential equations of parabolic type with nonlinearity, describing chemotaxis phenomena. The unknown functions of the system \(u\), \(v\) and \(w\) represent the densities of two interacting populations and, respectively, the concentration of the common chemical attractant. The authors present very precise results of local and global existence in the frame of Besov spaces. Moreover, they prove analytic regularity with respect to the spatial variables. Basic tools in the proofs are dyadic decompositions, paraproduct techniques and Gevrey estimates as in [\textit{C. Foias} and \textit{R. Temam}, J. Funct. Anal. 87, No. 2, 359--369 (1989; Zbl 0702.35203)], see also \textit{H. A. Biagioni} and \textit{T. Gramchev} [J. Differ. Equations 194, No. 1, 140--165 (2003; Zbl 1160.35311)].
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 76A15
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 35B44
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 6848018
zbMATH Keywords: two-species chemotaxis system
zbMATH Keywords: Gevrey regularity
zbMATH Keywords: Besov spaces
zbMATH Keywords: blow-up criterion
zbMATH Keywords: Triebel-Lizorkin spaces
author: Minghua Yang
author: Zunwei Fu
author: Jinyi Sun
MaRDI profile type: Publication
full work available at URL: s11425-016-0490-y
OpenAlex ID: W2621440818
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Existence and Gevrey regularity for a two-species chemotaxis system in homogeneous Besov spaces (DOI)
DOI: 10.1007/S11425-016-0490-Y

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