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Suppression of chemotactic singularity by buoyancy

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arxiv 2305.01036 v2 pith:XM6IJXKY submitted 2023-05-01 math.AP

Zhongtian Hu , Alexander Kiselev , Yao Yao This is my paper · ORCID
classification math.AP
keywords fluidsingularityformationadvectionbuoyancychemotacticcouplingequation
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Chemotactic singularity formation in the context of the Patlak-Keller-Segel equation is an extensively studied phenomenon. In recent years, it has been shown that the presence of fluid advection can arrest the singularity formation given that the fluid flow possesses mixing or diffusion enhancing properties and its amplitude is sufficiently strong - this effect is conjectured to hold for more general classes of nonlinear PDEs. In this paper, we consider the Patlak-Keller-Segel equation coupled with a fluid flow that obeys Darcy's law for incompressible porous media via buoyancy force. We prove that in contrast with passive advection, this active fluid coupling is capable of suppressing singularity formation at arbitrary small coupling strength: namely, the system always has globally regular solutions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Strong solutions to the Keller-Segel-Navier-Stokes system in bounded Lipschitz domains

    math.AP 2025-05 accept novelty 7.0 of 10

    Local and global strong well-posedness, exponential stability, global boundedness, and positivity for Keller-Segel-Navier-Stokes and chemotaxis-consumption systems on bounded Lipschitz domains in critical Besov spaces.

  2. On the sharp critical mass threshold for the 3D Patlak-Keller-Segel-Navier-Stokes system via Couette flow

    math.AP 2025-06 conditional novelty 6.0 of 10

    For the 3D Patlak-Keller-Segel-Navier-Stokes system near a strong Couette flow, global regularity is proved for initial cell mass below 16π².

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