Decay estimates for the classical solution of Keller–Segel system with fractional Laplacian in higher dimensions

ABSTRACT

In this paper, we investigate the generalized Keller–Segel system with two fractional parabolic equations and a classical elliptic equation in ${\mathbb{R}}^n$ with $n⩾2$. We develop a framework for a unified treatment of the existence, uniqueness and decay estimates. With the help of selecting appropriate functional space, the existence, uniqueness and decay estimates of the global classical solution are shown at the same time under the assumption that the initial data are small enough.

COMMUNICATED BY:

• Scott Hansen

KEYWORDS:

• Keller–Segel system
• fractional Laplacian
• global classical solution
• decay estimates

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35A01
• 35B40
• 35H10
• 35K55

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by National Natural Science Foundational of China [11771380 and 11401515].