11-10U

We propose a consistent statistical description of kinetics and hydrodynamics of dusty plasma based on the Zubarev nonequilibrium statistical operator method. The nonequilibrium statistical operator and the generalized transport equations for a consistent description of kinetics of dust particles and hydrodynamics of electrons, ions and neutral atoms are obtained for the cases of conservative and partial dynamics. In the approximation of weak nonequilibrium a spectrum of collective excitations of dusty plasma in the hydrodynamic limit is investigated by means of perturbation theory for collective modes.