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Main Author: He, Siming
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2405.06048
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author He, Siming
author_facet He, Siming
contents In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) 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.
format Preprint
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institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows
He, Siming
Analysis of PDEs
In this study, we investigate the behavior of three-dimensional parabolic-parabolic Patlak-Keller-Segel (PKS) 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.
title Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part II: Shear Flows
topic Analysis of PDEs
url https://arxiv.org/abs/2405.06048