Analysis of a model describing bacterial colony expansion in radial geometry driven by chemotaxis

We investigate a recent model proposed in the literature elucidating patterns driven by chemotaxis, similar to vis-cous fingering phenomena. Notably, this model incorporates a singular advection term arising from a modifiedformulation of Darcy's law. It is noteworthy that this type of advection can also be well interpreted as a descriptionof a radial fluid flow source surrounding an aggregation of cells. For the two-dimensional scenario, we establish aprecise threshold delineating between blow-up and global solution existence. This threshold is contingent upon thepressure magnitude and the initial total mass of the aggregating cells.