Hydrodynamic model for the system of self propelling particles with conservative kinematic constraints; two dimensional stationary solutions

In a first paper we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. [Phys. Rev. Lett. 75 (1995) 1226]. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional.