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We use the method of the microscopic phase density to get the kineticequation for the system of self-propelled particles with Vicsek-like alignmentrule. The hydrodynamic equations are derived for the ordered phase taking intoaccount the mean-field force only. The equation for the hydrodynamic velocityplays the role of the Euler equation for the self-propelled Vicsek fluid. Thehydrodynamics of such ideal self-propelled fluid demonstrates the dynamicaltransition from disordered initial state to the completely ordered motion. Totake the noise into account we consider how the framework of the localequilibrium approximation affects the hydrodynamic equations and the viscoustensor and show that in such approximation the shear viscosity vanishes.

physica a statistical mechanics and its applications

The microscopic phase density functional approach to the construction of  the kinetic and hydrodynamic description for the system of self-propelled  particles