In our previous papers we proposed a continuum model for the dynamics of the
systems of self-propelling particles with conservative kinematic constraints on
the velocities. We have determined a class of stationary solutions of this
hydrodynamic model and have shown that two types of stationary flow, linear and
radially symmetric (vortical) flow, are possible. In this paper we consider the
stability properties of these stationary flows. We show, using a linear
stability analysis, that the linear solutions are neutrally stable with respect
to the imposed velocity and density perturbations. A similar analysis of the
stability of the vortical solution is found to be not conclusive.Comment: 13 pages, 3 figure