Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms

Espejo, Elio and Wu, Hao (2020) Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms. Communications in Mathematical Sciences, 18 (2). pp. 379-394. ISSN 15396746

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Abstract

Our aim is to show that several important systems of partial differential equations arising in mathematical biology, fluid dynamics and electrokinetics can be approached within a single model, namely, a Keller-Segel-type system with rotational flux terms. In particular, we establish sharp conditions on the optimal critical mass for having global existence and finite time blow-up of solutions in two spatial dimensions. Our results imply that the rotated chemotactic response can delay or even avoid the blow-up. The key observation is that for any angle of rotation α∈(-π, π], the resulting PDE system preserves a dissipative energy structure. Inspired by this property, we also provide an alternative derivation of the general system via an energetic variational approach. ©2020 International Press.

Item Type: Article
Keywords: chemotaxis; rotational flux; critical mass; blow-up; global existence; dissipative energy structure.
Schools/Departments: University of Nottingham Ningbo China > Faculty of Science and Engineering > School of Mathematical Sciences
Identification Number: https://doi.org/10.4310/CMS.2020.v18.n2.a5
Depositing User: QIU, Lulu
Date Deposited: 19 Aug 2020 07:52
Last Modified: 19 Aug 2020 07:52
URI: http://eprints.nottingham.ac.uk/id/eprint/61342

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