On the dynamics of dilute gases

The evolution of a gas can be described by different mathematical models depending on the scale observation. A natural question, raised Hilbert in his sixth problem, is whether these provide mutually consistent predictions. In particular, for rarefied gases, it expected that equations kinetic theory gases obtained from molecular dynamics governed fundamental principles mechanics. case hard sphere Lanford (1975) has shown Boltzmann equation does indeed appear as law large numbers low density limit, at least very short times. aim this paper to present recent advances understanding limiting process.