Compatibility criteria for generalized Boltzmann equations

It is suggested that long-range correlations in a rarefied gas can be described by a hierarchy of generalized Boltzmann equations which, unlike either the Liouville equation or the BBGKY hierarchy, take the rarefaction of the gas into account and are presumably easier to handle. The equations are postulated, and compatibility criteria for their truncation as well as a class of truncations are proposed. The work presented here can be regarded as a further step toward a kinetic theory of turbulence (for rarefied gases) along the lines of Zhigulev (1966) and Tsuge(1970).