Derivation of slip boundary conditions for the Navier-Stokes system from the Boltzmann equation (Q1116806)

Rarefied gas flow behavior is usually described by the Boltzmann equation, the Navier-Stokes system being valid when the gas is less rarefied. Slip boundary conditions for the Navier-Stokes equations are derived in a rigorous and systematic way from the boundary condition at the kinetic level (Boltzmann equation). These slip conditions are explicitly written in terms of asymptotic behavior of some linear half- space problems. The validity of this analysis is established in the simple case of the Couette flow, for which it is proved that the right boundary conditions are obtained.