Suppression of Chemotactic Singularity via Viscous Flow with Large Buoyancy

Abstract

In this work, we study the Keller-Segel-Navier-Stokes equation with low Reynolds number and subject to large buoyancy force. We show that for initial cell density with arbitrarily large mass (i.e. the $L^1$ norm), the solution remains regular for all times in the regime of sufficiently large buoyancy and viscosity. The major blowup suppression mechanism is a norm-stabilizing property possessed by a ``static problem,'' where the full problem can be seen as a perturbation of this quasi-stationary model.