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

Elio Espejo, Hao Wu

Research output: Journal PublicationArticlepeer-review

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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.
Original languageEnglish
Pages (from-to)379-394
JournalCommunications in Mathematical Sciences
Volume18
Issue number2
DOIs
Publication statusPublished - 17 Jan 2020

Keywords

  • chemotaxis
  • rotational flux
  • critical mass
  • blow-up
  • global existence
  • dissipative energy structure.

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