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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 3
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Articles

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

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Pages 447-461 | Received 28 Jan 2018, Accepted 09 Jul 2018, Published online: 25 Jul 2018
 

ABSTRACT

In this paper, we investigate the generalized Keller–Segel system with two fractional parabolic equations and a classical elliptic equation in Rn with n2. 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.

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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].

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