Work

Time-dependent shear flows and their applications in parabolic–parabolic Patlak–Keller–Segel systems*

Year: 2025

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.

Source: Nonlinearity

DOI: 10.1088/1361-6544/adba35

Author: Siming He

Institution: University of South Carolina

Language: English

Topic: Mathematical Biology Tumor Growth

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funder: Division of Mathematical Sciences