JournalszaaVol. 37, No. 4pp. 417–433

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

  • Xiaoli Chen

    Jiangxi Normal University, Nanchang, China
Well-Posedness of the Keller–Segel System in Fourier–Besov–Morrey Spaces cover
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Abstract

In this note, we investigate the Cauchy problem for Keller–Segel system with fractional diffusion for the initial data (u0,v0)(u_0,v_0) in the critical Fourier–Bessov–Morrey spaces FNq,μ,r22α+ddμq(Rd)×FNq,μ,r2α+ddμq(Rd)\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<α21 < \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.

Cite this article

Xiaoli Chen, Well-Posedness of the Keller–Segel System in Fourier–Besov–Morrey Spaces. Z. Anal. Anwend. 37 (2018), no. 4, pp. 417–433

DOI 10.4171/ZAA/1621