  We study boundary conditions applied to the macroscopic dynamics of Newtonian
liquids from the view of microscopic particle systems. We assume the existence
of microscopic boundary conditions that are uniquely determined from a
microscopic description of the fluid and the wall. By using molecular dynamical
simulations, we examine a possible form of the microscopic boundary conditions.
In the macroscopic limit, we may introduce a scaled velocity field by ignoring
the higher order terms in the velocity field that is calculated from the
microscopic boundary condition and standard fluid mechanics. We define
macroscopic boundary conditions as the boundary conditions that are imposed on
the scaled velocity field. The macroscopic boundary conditions contain a few
phenomenological parameters for an amount of slip, which are related to a
functional form of the given microscopic boundary condition. By considering two
macroscopic limits of the non-equilibrium steady state, we propose two
different frameworks for determining macroscopic boundary conditions.
