Suppression of Chemotactic Blowup by Strong Buoyancy in Stokes-Boussinesq Flow with Cold Boundary

TL;DR

This paper demonstrates that strong buoyancy coupling in a Stokes-Boussinesq flow prevents chemotactic blowup, ensuring global regularity and quenching the dynamics after a finite time, contrasting with blowup in the absence of flow.

Contribution

It introduces a novel coupling mechanism that suppresses chemotactic blowup in Keller-Segel equations through strong buoyancy effects in Stokes-Boussinesq flow.

Findings

Strong buoyancy coupling enforces global regularity.

Flow coupling quenches chemotactic blowup.

Without flow, finite-time singularities occur.

Abstract

In this paper, we show that the Keller-Segel equation equipped with zero Dirichlet Boundary condition and actively coupled to a Stokes-Boussinesq flow is globally well-posed provided that the coupling is sufficiently large. We will in fact show that the dynamics is quenched after certain time. In particular, such active coupling is blowup-suppressing in the sense that it enforces global regularity for some initial data leading to a finite-time singularity when the flow is absent.