The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (312 KB) | Metadata | Table of Contents | ZAA summary
Online access to the full text of Zeitschrift für Analysis und ihre Anwendungen is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Volume 37, Issue 4, 2018, pp. 417–433
DOI: 10.4171/ZAA/1621

Published online: 2018-10-18

Well-Posedness of the Keller–Segel System in Fourier–Besov–Morrey Spaces

Xiaoli Chen[1]

(1) Jiangxi Normal University, Nanchang, China

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 $1 < \alpha\le 2$. The global well-posedness with a small initial data of the solution to Keller–Segel system of double-parabolic type is established.

Keywords: Keller-Segel system, fractional diffusions, Littlewood-Paley theory, Fourier–Besov space, well-posedness

Chen Xiaoli: Well-Posedness of the Keller–Segel System in Fourier–Besov–Morrey Spaces. Z. Anal. Anwend. 37 (2018), 417-433. doi: 10.4171/ZAA/1621