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In this paper, we give sufficient conditions for global-in-time existence ofclassical solutions for the fully parabolic chemorepulsion system posed on aconvex, bounded three-dimensional domain. Our main result establishesglobal-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 theBakry--\'Emery calculation and appears to be new in this context.

On the existence of global solutions for the 3D chemorepulsion system