  Chemotactic singularity formation in the context of the Patlak-Keller-Segel
equation is an extensively studied phenomenon. In recent years, it has been
shown that the presence of fluid advection can arrest the singularity formation
given that the fluid flow possesses mixing or diffusion enhancing properties
and its amplitude is sufficiently strong - this effect is conjectured to hold
for more general classes of nonlinear PDEs. In this paper, we consider the
Patlak-Keller-Segel equation coupled with a fluid flow that obeys Darcy's law
for incompressible porous media via buoyancy force. We prove that in contrast
with passive advection, this active fluid coupling is capable of suppressing
singularity formation at arbitrary small coupling strength: namely, the system
always has globally regular solutions.
