Well-posedness of the Keller-Segel system in Fourier-Besov-Morrey spaces
type: Item
instance of: scholarly article
title: Well-posedness of the Keller-Segel system in Fourier-Besov-Morrey spaces
zbMATH Open document ID: 1402.35141
DOI: 10.4171/ZAA/1621
author: Xiaoli Chen
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2018-11-15T00:00:00Z
review text: Summary: In this note, we investigate the Cauchy problem for Keller-Segel system with fractional diffusion for the initial data \((u_0,v_0)\) in the critical Fourier-Bessov-Morrey spaces \(\mathcal{FN}_{q,\mu,r}^{2-2\alpha+d-\frac{d-\mu}{q}}(\mathbb R^d)\times \mathcal{FN}_{q,\mu,r}^{2-\alpha+d-\frac{d-\mu}{q}}(\mathbb R^d)\) with \(1 < \alpha\leq 2\). The global well-posedness with a small initial data of the solution to Keller-Segel system of double-parabolic type is established.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 47J35
zbMATH DE Number: 6979889
zbMATH Keywords: Keller-Segel system
zbMATH Keywords: fractional diffusions
zbMATH Keywords: Littlewood-Paley theory
zbMATH Keywords: Fourier-Besov space
zbMATH Keywords: well-posedness
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1621
OpenAlex ID: W2895943016
Wikidata QID: Q129067496
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description: scientific article; zbMATH DE number 6979889