NONLOCAL BOUNDARY CONDITIONS FOR THE NAVIER-STOKES EQUATIONS

摘要

In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the hydrodynamic limit. Basing on phenomenological arguments, two scattering kernels which model non-local interactions between the gas molecules and the wall boundary are proposed. They satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a new class of nonlocal boundary conditions.