  In this paper, we give sufficient conditions for global-in-time existence of
classical solutions for the fully parabolic chemorepulsion system posed on a
convex, bounded three-dimensional domain. Our main result establishes
global-in-time existence of regular nonnegative solutions provided that
$\nabla\sqrt{u} \in L^4(0, T; L^2(\Omega))$. Our method is related to the
Bakry--\'Emery calculation and appears to be new in this context.
