  In this study, we investigate the behavior of three-dimensional
parabolic-parabolic Patlak-Keller-Segel (PKS) systems in the presence of
ambient shear flows. Our findings demonstrate that when the total mass of the
cell density is below a specific threshold, the solution remains globally
regular as long as the flow is sufficiently strong. The primary difficulty in
our analysis stems from the fast creation of chemical gradients due to strong
shear advection.
