  We consider the singular limit of a chemotaxis model of bacterial collective
motion recently introduced in arXiv:2009.11048 [math.AP]. The equation models
aggregation-diffusion phenomena with advection that is discontinuous and
depends sharply on the gradient of the density itself. The quasi-linearity of
the problem poses major challenges in the construction of the solution and
complications arise in the proof of regularity. Our method overcomes these
obstacle by relying solely on entropy inequalities and the theory of monotone
operators. We provide existence, uniqueness and smoothing estimates in any
dimensional space.
