Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms
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...
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| Format: | Article |
| Language: | English |
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2020
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| Online Access: | https://eprints.nottingham.ac.uk/61342/ |
| _version_ | 1848799863047716864 |
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| author | Espejo, Elio Wu, Hao |
| author_facet | Espejo, Elio Wu, Hao |
| author_sort | Espejo, Elio |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:42:25Z |
| format | Article |
| id | nottingham-61342 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:42:25Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-613422020-08-19T07:52:45Z https://eprints.nottingham.ac.uk/61342/ Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms Espejo, Elio Wu, Hao 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. 2020-01-17 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/61342/1/ilovepdf_merged%20%284%29.pdf 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 chemotaxis; rotational flux; critical mass; blow-up; global existence; dissipative energy structure. http://dx.doi.org/10.4310/CMS.2020.v18.n2.a5 doi:10.4310/CMS.2020.v18.n2.a5 doi:10.4310/CMS.2020.v18.n2.a5 |
| spellingShingle | chemotaxis; rotational flux; critical mass; blow-up; global existence; dissipative energy structure. Espejo, Elio Wu, Hao Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms |
| title | Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms |
| title_full | Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms |
| title_fullStr | Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms |
| title_full_unstemmed | Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms |
| title_short | Optimal critical mass for the two-dimensional Keller–Segel model with rotational flux terms |
| title_sort | optimal critical mass for the two-dimensional keller–segel model with rotational flux terms |
| topic | chemotaxis; rotational flux; critical mass; blow-up; global existence; dissipative energy structure. |
| url | https://eprints.nottingham.ac.uk/61342/ https://eprints.nottingham.ac.uk/61342/ https://eprints.nottingham.ac.uk/61342/ |