06-24U

A systematic approach to derivation of hydrodynamic transport equations based on the BBGKY hierarchy is presented. Cases of many-particle local and two-particle nonlocal hydrodynamic densities are considered and explicit expressions for contributions of different types to their fluxes as well as sources are given. The scheme is applied to the set of conserved quantities. Equations for their fluxes are obtained, which form the first extension of the usual hydrodynamics. Principal possibility of next extensions resulting in an infinite hierarchy of equations of hydrodynamic type is predicted. Explicit transport equations for the stress tensor and the heat flux vector in the local frame of reference are written.