Enhanced dissipation and blow-up suppression in a chemotaxis-fluid system

TL;DR

This paper demonstrates that shear flow mixing induces enhanced dissipation in a chemotaxis-fluid system, preventing blow-up and ensuring global regularity even with large cell populations.

Contribution

It introduces a novel mechanism showing how shear flow mixing suppresses blow-up in a coupled chemotaxis-fluid model, ensuring global solutions.

Findings

Shear flow induces enhanced dissipation in the PKS-NS system.

Global regular solutions exist for large cell populations.

Shear flow prevents finite-time blow-up in the model.

Abstract

In this paper, we investigate a coupled Patlak-Keller-Segel-Navier-Stokes (PKS-NS) system. We show that globally regular solutions with arbitrary large cell populations exist. The primary blowup suppression mechanism is the shear flow mixing induced enhanced dissipation phenomena.