Document Type
Article
Abstract
In this study, we investigate the behavior of three-dimensional parabolic–parabolic Patlak–Keller–Segel systems in the presence of ambient shear flows. Our findings demonstrate that when the total mass of the cell density is below a specific threshold, the solution remains globally regular as long as the flow is sufficiently strong. The primary difficulty in our analysis stems from the fast creation of chemical gradients due to strong shear advection.
Digital Object Identifier (DOI)
Publication Info
Published in Nonlinearity, Volume 38, Issue 3, 2025, pages 035029-.
APA Citation
He, S. (2025). Time-dependent shear flows and their applications in parabolic–parabolic Patlak–Keller–Segel systems*. Nonlinearity, 38(3), 035029.https://doi.org/10.1088/1361-6544/adba35
Rights
© 2025 The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.