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Suppression of chemotactic blow-up by buoyancy

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Authors : Yao, Yao (Author of the conference)
CIRM (Publisher )

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Abstract : Chemotactic blow up in the context of the Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that when the Keller-Segel equation is coupled with passive advection, blow-up can be prevented if the flow possesses mixing or diffusion-enhancing properties, and its amplitude is sufficiently strong. In this talk, we consider the Keller-Segel equation coupled with an active advection, which is an incompressible flow obeying Darcy's law for incompressible porous media equation and driven by buoyancy force. We prove that in contrast with passive advection, this active advection coupling is capable of suppressing chemotactic blow up at arbitrary small coupling strength: namely, the system always has globally regular solutions. (Joint work with Zhongtian Hu and Alexander Kiselev).

Keywords : Chemotaxis; Darcy's law; blow-up suppression

MSC Codes :
35B35 - Stability of solutions of PDE
35K55 - Nonlinear parabolic equations
76B03 - Existence, uniqueness, and regularity theory

Additional resources :
https://www.cirm-math.fr/RepOrga/3049/Slides/Yao_Yao_CIRM.pdf

    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 30/04/2024
    Conference Date : 11/04/2024
    Subseries : Research School
    arXiv category : Analysis of PDEs
    Mathematical Area(s) : PDE
    Format : MP4 (.mp4) - HD
    Video Time : 00:47:52
    Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
    Download : https://videos.cirm-math.fr/2024-04-11_Yao.mp4

Information on the Event

Event Title : Aggregation-Diffusion Equations & Collective Behavior: Analysis, Numerics and Applications / Conférence Chaire Jean Morlet: Equations d'agrégation-diffusion et comportement collectif: Analyse, schémas numériques et applications
Event Organizers : Carrillo, José Antonio ; Esposito, Antonio ; Gómez-Castro, David ; Nouri, Anne
Dates : 08/04/2024 - 12/04/2024
Event Year : 2024
Event URL : https://conferences.cirm-math.fr/3049.html

Citation Data

DOI : 10.24350/CIRM.V.20160403
Cite this video as: Yao, Yao (2024). Suppression of chemotactic blow-up by buoyancy. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20160403
URI : http://dx.doi.org/10.24350/CIRM.V.20160403

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