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Zeitschrift für Analysis und ihre Anwendungen


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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