Asymptotic methods in kinetic theory of gases: An introduction (Part 2)

Part 2 : In this part, we consider the near continuum regime (or near the fluid-dynamic limit), i.e., the case where the mean free path is small compared with the characteristic length. We show the outline of the formal asymptotic analysis of the steady boundary-value problem of the Boltzmann equation that provides the fluid-dynamic type equations, their boundary conditions of slip type, and the kinetic correction to fluid-dynamic solutions in the vicinity of the boundary (the Knudsen layer) systematically. A special emphasis is put on the case in which the fluid-dynamic limit thus obtained is not covered by the conventional fluid dynamics (the ghost effect).