Averaging out Inhomogeneous Newtonian Cosmologies: I. Fluid Mechanics and the Navier-Stokes Equation

The basic concepts and equations of classical fluid mechanics are presented in the form necessary for the formulation of Newtonian cosmology and for derivation and analysis of a system of the averaged Navier-Stokes-Poisson equations. A special attention is paid to the analytic formulation of the definitions and equations of moving fluids and to their physical content.