Suppression of Chemotactic Singularity via Viscous Flow with Large Buoyancy
In this work, we study the Keller-Segel equation coupling to the (Navier-)Stokes equation with low Reynolds number and Lions boundary condition. The coupling of both equations is realized via a buoyancy force. We show that for initial cell density with arbitrarily large mass, 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 static model.