Suppression of blow-up in Patlak–Keller–Segel–Navier–Stokes system via the Couette flow in whole space
Abstract
Abstract This paper studies the two-dimensional Patlak–Keller–Segel–Navier–Stokes (PKS–NS) system in R 2 ${\mathbb{R}}^{2}$ near the Couette flow ( Ay , 0). Using the Green’s function method, we first derive enhanced dissipation estimates for the linearized system around this background flow. As a key application, we prove that solutions remain globally regular provided the shear rate A is sufficiently large.
Fields of Study & Subjects
Navier-Stokes equation solutions
Mathematical Biology Tumor Growth
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Advances in Nonlinear Analysis
- Volume
- 15
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN