Derivation of the Hydrodynamic Equations in the Framework of the Bogoliubov Functional Hypothesis

We generalize the Bogoliubov functional hypothesis to the case of multiparticle interaction depending on both the coordinates and momenta of particles. We illustrate this with the examples of two weakly relativistic models: the Darwin model in the theory of charged particles and the Fock model in the general theory of relativity. For these models, based on the chain of the BBGKY equations, we calculate weakly relativistic corrections to the classical transport coefficients and find the conditions under which there is no bijective relation between the parameters of the local equilibrium distribution and the hydrodynamic variables.