Aggregated Steady States of a Kinetic Model for Chemotaxis
  A kinetic chemotaxis model with attractive interaction by quasistationary chemical signalling is considered. The special choice of the turning operator, with velocity jumps biased towards the chemical concentration gradient, permits closed ODE systems for moments of the distribution function of arbitrary order. The system for second order moments exhibits a critical mass phenomeneon. The main result is existence of an aggregated steady state for supercritical mass. 
Anne Nouri, Christian Schmeiser
math.AP